In my experience, Canson Platine Fiber Rag and Hahnemuhle Photo Rag Baryta are very similar papers in look, feel and performance. There are slight differences in surface texture, but they're close enough to each other that if you like/dislike one you'll probably feel the same about the other. IMHO they're far closer to each other than to any other papers I've tested. Both have a very white paper base for being OBA free, and I can't say that I've noticed any difference between the two in gloss differential (though this isn't something I've looked closely for, since in my experience its rarely if ever a problem with the Canon inks and today's semi-gloss papers).
The one difference in performance is that the Hahnemuhle paper has a slightly better DMax, which also allows it to have better gamut in the darker tones for color prints. This is pretty much my only reason for having a preference for the Hanemuhle Paper despite its slightly higher price; since darker, saturated colors reproduce a little better. But both papers are really nice. In the end my final preference may come down to seeing how permanence ratings for these two papers come out at AA&I (I've already submitted samples of Photo Rag Baryta for testing, and will probably submit samples of the Canson if somebody doesn't beat me to it).
BTW my experience with these papers is using a Canon 6300 with the Lucia EX inkset, I suppose it's possible that results could be slightly different with other inksets.