I was wondering if the constellations visible from Earth would also be visible from Mars. Would they look the same but just shifted slightly in the sky due to the larger circumference of the orbit?
The stars are so immensely far away that to the human eye there would be no noticeable difference. The nearest stars are moving roughly 1.5 arcsecond wrt. the background when viewed from Earth's position with half a year's interval (i.e. half a revolution around the Sun). Mars' orbit is only 50% larger, but the human eye cannot resolve better than roughly one arcminute.
However, the sky would look different for another reason: Although stars are point sources, on Earth stars are smeared out due to the atmosphere. On Mars, there's almost no atmosphere, but on the other hand there's lots of dust whirling around. Dust tends to absorb blue light more than red and thus redden objects. However, Martian dust happens to scatter red more than blue (Ockert-Bell et al. 1997), so the stars should appear more blue. Also, the dust will scatter the Sun's light so much that no stars are visible during the day (as opposed to e.g. the Moon). Note also that the north pole of Mars points not toward Polaris, but toward Deneb in Cygnus.
Since a shift in position of 1 AU (the distance from Earth to the Sun) corresponds to a shift in position of 1 arcsec for a star which is 1 pc (3.26 lightyears) away, if you want to go to a place where the nearest star (Proxima Centari; 1.3 pc away) has moved a full moon diameter, i.e. ½ a degree — you would need to travel roughly 2340 AU away, i.e. much farther away than Pluto, but still inside the Solar system.
Most stars are much farther away, however. The brightest stars that give the constellations their appearance are tens to hundreds of pc away, so to really change the constellation, you should go 10 or 100 times farther away, i.e. roughly 1 pc. In other words, the constellation will look (slightly, but conspicuously) different from out nearest neighbor stars.