There are two achievements based on which faction you side for, those being:
1. Hero of the Resistence (siding with the Resistance)
2. Man of Honour (siding with Honour Grant)
No matter who you choose, this achievement will pop. However, I recommend creating a save beforehand to collect the other two achievements that aren't part of it. There's no direct benefit from siding with one or the other, besides the change of companions. This is also the time that the mentor achievement should pop as well.