One reason that microgravity may be beneficial for reaching a lower temperature for laser-cooled atoms may be the following. In many ultracold atom experiments, usually after initial laser cooling, ultracold temperature is obtained by evaporative cooling (i.e. remove hot atoms from your sample, and they take away extra thermal energy, thereby cooling the sample overall), which is done in a tight confining potential to have high elastic collision (and thus thermalization) rate. Then the sample can be adiabatically decompressed into a shallower trap, reducing the temperature even more. However, as you make final confining potential shallower/flatter, the gravitational potential will eventually dominate. This is one way gravity can be a limit on the temperature of the trapped ultracold atomic gas.
Another benefit of microgravity, especially for atomic fountain clocks, is a longer interrogation time. Because gravity is weak, atoms that are tossed up vertically take much longer time to return back to the original position, and the resulting longer interrogation time reduces the frequency uncertainty of your atomic clock further.
EDIT: I think the answer to the question you have linked gives a similar answer as I have written in my first paragraph, and that answer also contains a link to the research resulting in the coldest temperature achieved by the gravito-magnetic trap for ultracold atoms (by Wolfgang Ketterle). Also, as dolan has nicely explained, there are limits to how you can compensate gravity using magnetic gradients (e.g. non-zero curvature, state selectivity, etc.)