Are there any old/ancient star maps that we can compare to today’s and see drastic differences?
Yes, we can! Well, depending on some definitions (e.g. “star”, “map”, “drastic”).
The universe is not static (see Big Bang), everything is moving, space is expanding, stars are born, live, age, and die (see stellar evolution). Thus, we do have changes. And we are able to observe them – observation led to the theories given above. “Observe” does not necessarily mean “see with the naked eyes”, though. (It can even mean “deduce from observing a large number of objects of the same type”.) The changes generally happen at an astronomical time scale, see the answer of Lariliss. Therefore, generally the changes in one human lifetime or even several of those are too small to be seen (but see below). (If “map” means “astronomical catalogue”, position changes are seen therein.)
“old/ancient star maps”, as I understand it, are not about the position of stars in the universe! First, it is not about stars at all. “A star is an astronomical object consisting of a luminous spheroid of plasma held together by its own gravity” (https://en.wikipedia.org/wiki/Star). That is not what an ancient star map would record. That ancient star map would record visible (luminous/light reflecting/…) “dots” in the night sky. This excludes our Sun, although it is a star (by the recent definition), but includes for example supernovae (former stars), novae, comets, asteroids, nebula, other planets in our solar system, our Moon, to name a few. Changes in the observation of those objects can be seen in much shorter time spans. The (super-)novae are explicitly named such, i.e. nova meaning new (star, although it is not a new star but a bright dot in the night sky where before there was no dot visible). When “map” means “depiction of luminous dots in the night sky”, then there would be maps without the (super-)nova, and later maps with it, maps showing a comet and maps not showing it. The Moon changes from “new” (i.e. completely dark) to full to new in one lunar month. The other planets circle the Sun not synchronized to the Earth circling the Sun, thus changing their position in the sky. Comets come and go, and some come again (see https://en.wikipedia.org/wiki/List_of_periodic_comets). Thus there are observable changes.
Another point is that the “old/ancient star maps” would not record the positions of those dots in the universe, but the observed, apparent positions on the sky. There are drastic changes of the apparent positions due to changes of the position of the observer. Movement of the observer does not mean traveling from north to south pole (which would also lead to quite different observations, see Northern and Southern celestial hemisphere) but sitting down at one point of the surface of the Earth and letting the Earth do all the motion. So, what does the Earth do to the unsuspecting observer of the sky? https://courses.lumenlearning.com/astronomy/chapter/the-sky-above/ gives some good explanations (and figures!):
Earth rotates around its own axis. This leads to (apparent!) rise and down of Sun, Moon, “stars” (meaning dots in the night sky). “As Earth rotates about its axis, the sky appears to turn in the opposite direction around those celestial poles (Figure 3)” at https://courses.lumenlearning.com/astronomy/chapter/the-sky-above/. Photographs of the night sky at different times of one night show quite different positions of the “stars”.
Earth rotates around the Sun (OK, around the common centre of gravity of Sun and Earth, which lays in the Sun but not in the centre of the Sun, happy now?) in one sidereal year. When positioned at the Earth’ poles, that does not drastically change your direction of view. But when positioned at the equator, you would look in quite the opposite direction (very simple model, not drawn to scale):
And in the opposite direction there are different “stars”, i.e. during the year the “stars” seem to move, see Figure 5: Constellations on the Ecliptic of https://courses.lumenlearning.com/astronomy/chapter/the-sky-above/. Photographs of the night sky at different times of the year show different stars. (Please do not stand at the poles just do disprove this, otherwise I will point out the parallax.)
And this is not complicated enough: The rotational axis of the Earth, the obliquity, is tilted and even “oscillates between 22.1 and 24.5 degrees on a 41,000-year cycle“ (ibid.). Thus a change of the tilt moves the position of the horizon against the celestial sphere, and a star, which was just barely visible above the horizon might vanish below it over the years. I remember reading about a “star map” drawn on a wall of a historic building (age: around 1,500 years), where that happened, but I do not remember the source.
And this is not complicated enough: The axis shows Axial precession: “In astronomy, axial precession is a gravity-induced, slow, and continuous change in the orientation of an astronomical body's rotational axis. In particular, it can refer to the gradual shift in the orientation of Earth's axis of rotation in a cycle of approximately 26,000 years.” This again leads to apparent movement of stars, see https://en.wikipedia.org/wiki/Axial_precession#History, shift of the equinox and (!) shift of the zodiac:
“There are two different zodiacs which divide the ecliptic into twelve
zodiac signs: the tropical zodiac with twelve sections, each with a
30° arc on the ecliptic, which is astronomically oriented to the
equinoxes and solstices, and the sidereal zodiac, which is oriented to
the - differently sized - constellations in the area of the ecliptic.
When the astrological system was developed in Hellenistic Alexandria,
probably from the 3rd century BC onwards, the tropical and sidereal
zodiacs still largely coincided, because the stars were equated as
indicators of the seasons. Compared to that time, however, the two
zodiacs today are about 30° out of phase with each other. So if, for
example, the Sun is currently in the zodiac sign of Capricorn at the
beginning of January, it is spatially in the constellation of
Sagittarius. The reason for this is that the Earth's axis, which is
decisive for the seasons, lurches - similar to a spinning top, but
very slowly, namely one round in about 25,800 years; this process is
known as precession. From the Earth's point of view, the point of
Aries moves backwards through the constellations of different sizes at
a speed of 1° in about 72 years.” (translated from https://de.wikipedia.org/wiki/Tierkreiszeichen#Tropischer_und_siderischer_Tierkreis).
“the Sun is currently in the zodiac sign of Capricorn at the beginning of January, it is spatially in the constellation of Sagittarius” – that is a drastic, observable difference, isn’t it? 30° is quite big. And “one round in about 25,800 years” is no problem: “A 32,500 year old carved ivory Mammoth tusk could contain the oldest known star chart (resembling the constellation Orion). It has also been suggested that drawing on the wall of the Lascaux caves in France dating from 33,000 to 10,000 years ago could be a graphical representation of the Pleiades, the Summer Triangle, and the Northern Crown.” (https://en.wikipedia.org/wiki/History_of_astronomy#Early_history)
More “is” than “could” was in the 2nd millennium BC: “The oldest accurately dated star chart appeared in ancient Egyptian astronomy in 1534 BC. The earliest known star catalogues were compiled by the ancient Babylonian astronomers of Mesopotamia in the late 2nd millennium BC, during the Kassite Period (ca. 1531–1155 BC).” (https://en.wikipedia.org/wiki/Star_chart) 3,500 years before present allow for some (apparent) movement: 3,500 years/72 years is nearly 50°! Nevertheless it could be argued, that the constellations did not (apparently) move (in space), but are at the same place but at another time in the year, i.e. moved in time instead of space. Fun fact: The stars (this time talking about the luminous spheroids of plasma) are not even at the positions, where we see their light today – they were at those positions when they emitted the light, which reaches us today, and then moved away. For stars visible with the naked eye, farthest away is V762 Cassiopeiae in 16,308 light-years according to https://cosmoknowledge.com/farthest-star-you-can-see-with-the-unaided-eye/.
At https://en.wikipedia.org/wiki/Archaeoastronomy#Recreating_the_ancient_sky we read:
“Not only does the Earth rotate, it wobbles. The Earth's axis takes
around 25,800 years to complete one full wobble. The effect to the
archaeoastronomer is that stars did not rise over the horizon in the
past in the same places as they do today. Nor did the stars rotate
around Polaris as they do now. In the case of the Egyptian pyramids,
it has been shown they were aligned towards Thuban, a faint star in
the constellation of Draco. The effect can be substantial over
relatively short lengths of time, historically speaking. For instance
a person born on 25 December in Roman times would have been born with
the Sun in the constellation Capricorn. In the modern period a person
born on the same date would have the Sun in Sagittarius due to the
precession of the equinoxes.”
The alignment at Thuban instead of Polaris is not a map, but the pyramids are quite big, thus I think it counts.
And this is not complicated enough: There is also Apsidal precession, Stellar parallax, the Sun rotates around the centre of our galaxy, and our galaxy, the Milky Way, moves in our Local Group, which also moves. There is also the apparent movement of the position of stars, which for real is the deflection of light by a mass, which the light passes (see e.g. Eddington experiment and Gravitational lens).
We have (apparent) change of position of stars (et al.), ancient viewed positions are shown to be different from recent ones. The question in the text below the title of OP’s question is somewhat different, Peter Erwin and Lariliss already answered that and Jacopo Tissino added the >>"map" (a statue, really) representing the stars as seen in, roughly, 125BCE<<. A paper (or papyrus or drawing in a tomb) remains to be found.