Having a spirit possess you doesn't affect your magic, edge, or mental abilities at all. A spirit possessing the mage who summoned it would use its own mental ability scores, or that of the host, whichever is lowest, I believe. And it would use its own magic and edge to deal with its powers. If the mage has channeling, he would use his own magic and edge, not the spirit's.
Summoning powerful spirits, whether it is a possession or normal tradition, is going to skew the odds heavily in your favor. That's just the nature of mages. However, the difference between the two is that with a normal tradition, you have two entities on the field (meaning yet another target to draw fire) taking two sets of actions according to their initiative. A mage summons a fire spirit, and then the mage can lightning bolt someone while the fire spirit flamethrowers the same guy, or someone else. With a possession tradition, a mage who has that fire spirit possess himself (even with Channeling) only has one entity on the field (albeit one that is largely immune to bullets) and only one set of actions. He can lightning bolt someone, or flamethrower them, but not both, and not at two different targets. Both are powerful, but both have weak spots and consume resources.