I've played Civ2 on both, but i never noticed a difference.
Civ2 is basically the same on both, but Civ1 is a world apart. The sprites are higher quality and the UI uses the standard Mac OS interface, so it scales nicely on higher res monitors (a lot of older Mac games did this, especially strategy games). On a more modern monitor you can pretty much see the entire map on screen at once. Managing your saves is easier because you can have 31 character file names, sort them in the Finder and launch them by double clicking the save files directly.
You might not think much of that, but back when I did a retrospective of the Civ series in the Ars Technica forums (not the crap ripoff posted on the front page by one of the staff) in the lead up to the release of Civ 5, I used the Windows version and the 8.3 filenames were a total nightmare compared to playing it my childhood. The Mac version's default save filenames have a structure of 2-4 letters indicating difficulty setting, your leader's name, and 6 characters for for the ingame date. The Windows version gives you 2 letters for leader name, 6 characters for date and a useless extension. Even playing on Vista enforce the 8.3 names. It makes it near impossible to keep your saves in any sort of order without making a separate subfolder for every game. Plus you had to load your saves via the ingame Windows 3.1 style dialog box. The Windows version does at least have the Mac version's other improvements and thus is superior to the DOS version.
Here's a screenshot of the Mac version from Moby.
If you allocate it more RAM you can drag that map window out to fully cover a 1920x1200 display. It's fantastic.
Only downside is there's less music, but what there is is high quality.