> Do other stars have similar gaseous-to-rocky ratios among their planets? For any given stellar system, are there typically as many gaseous planets as there are rocky planets?
With the current instruments and methods we have, we can only access certain population of exoplanets. Terrestrial-mass exoplanets are quite hard to find hence we have more discoveries of Jupiter-mass exoplanets, which does not mean that in reality, we have more chance to have a formation of Jupiter-mass, it just means that they are easier to detect so we detect more. Therefore it is hard to conclude and make statistics right now.
Or do most stars have either mostly gas giants or mostly rocky planets, making our own Solar system an exception?
This is more linked to planetary formation. I invite you to read about the 'core accretion model'. It explains very well the formation of terrestrial and gaseous planets in the proto-planetary disk. But in general, both can form and our Solar System is not an exception, we just don't have the instruments to find a system like it for now.
For example, an alien with the same instruments as us that would study the Sun with the radial velocity method would only detect Jupiter, the other planet would be invisible to it.