I'm not sure now, after these have been around a while, the Baryta label means very much. After going through quite a few, I settled on PhotRag Baryta some time ago, as it had no OBAs, was a very neutral base, and the gloss differential and bronzing were minimal. Gloss differential is what kept me form using the Canson offerings, though I like their matte fine art papers. After some years of QC problems with PhotoRag Baryta, with Hahnemuhle's input I switched to PhotoRag Pearl, which performs equally well, but was flawless roll after roll. The difference between the papers is nearly impossible to detect, so the presence of baryta seems a negligible contribution to me. There are manufacturing reasons the one has problems the other does not, and I will not get into that here.
One little discussed baryta alternative paper I like a lot is Cone Type 5. It is a bit warmer, and has more texture, bit it's a very natural looking texture that avoids that fake manufactured surface. It also performs very well.
Lastly, I had a chance to test some of the Hahnemuhle Silk Baryta, and was very impressed, surface very natural, prints looked nice, did not have a blue OBA look.
Any other baryta or photo surface papers have fallen short, or I have not had sufficient experience with them for a sound conclusion.
I've run more PhotoRag Pearl than any other photo surface paper, the prints always look great, the gamut and dmax excellent, no quality problems at all. If I were printing more photo surface prints again, I'd run more of the Silk to get more experience over time, looked promising.
That's all I got....