So to sum it up:
1. First of all, FF armies are complete non factors, unless if you think that guys with swords can take space age soldiers with guns.
2. Mass Effect universe has FAR greater numbers.
3. Mass Effect universe has FAR greater economic power, with factories and stuff spread across the GALAXY.
4. Mass Effect universe has ships that launch shells 3 times the power of nuclear bombs with a range of hundreds of thousands of kilometers. Wait...actually, according to the codex, their guns actually have unlimited maxinum range in space and will go on indefinately until it hits a big enough object, so really, considering the large size of whatever planets that the FF forces live on, the Mass Effect ships could simply sit star systems away and hit it from a range in which the FF characters can do NOTHING to stop.
5. Final Fantasy has nothing to counter this, except for a few of the bosses...
5. ...many of which are beaten by the protagonist and his/her party, which consists of a few guys with swords/shields/some magic...
6. But all of this is irrelevant, because FF dudes don't have FTL tech, meaning that they have NO hope of actually invading Mass Effect universe. BTW, there is NO proof that teleportation = FTL.
7. Therefore, Mass Effect universe could simply wait for their tech to grow and then attack.
8. Or they simply glass the FF worlds into shreds from hundreds of thousands of miles away.
Either way, FF universe DIES horribly.