I do not think that Chaucer thinks either of these men leads a particularly good life. They are both part of the clergy -- a group that (Chaucer thinks) mostly lives off cheating the people. He does not think either of them is much of a man of God.
However, if you have to choose one, I think you should say that the Friar is living the better life. I think that he, at least, does some good to some people. The Friar makes his living by hearing confessions and taking payments for doing so. He's supposed to give the money away, but he doesn't. That's bad, but at least he is helping the people whose confessions he hears. At the very least, he is making them feel better.
By contrast, the Monk does not really do any kind of good for anyone except himself (and maybe for the Prioress whose estate he manages). All he does is make sure the estate is running well so he can go and hunt and do other fun stuff.
So both of them are in now way holy men. But at least the Friar makes some people feel good by hearing their confessions. The Monk does not even do that much.