Just to summarize some of the comments that have already been posted and also add some info that hasn't been mentioned yet:
Platine is OBA free and the base sheet is cotton fiber. Its coating uses TiO2 whitening agents not Barium sulfate. It exhibits a fine surface stipple with ever so slight grain orientation. The base sheet may therefore be mechanically calendared during production to make it smoother before it later gets the coatings added.
Canson Bartya Photographique has an alphacellulose base sheet and Barium sulfate whitening plus a moderately low level of OBA. Because the OBA amount is used with restraint, it significantly outperforms in light fade testing compared to papers with high OBA content like Epson Exhibition Fibre paper. CIFA Baryta is almost a "dead ringer" for Ilford Gold Fibre Silk but, IMHO, not identical. It appears to use same coating technology both front and back side. My guess is that the ever-so-slight difference between the two papers is due to Canson supplying the base sheet whereas IGFS base sheet is probably sourced from a different paper manufacturer or made with different calendaring/finishing procedures. That said, the apparently shared top coatings and anti-curl layer technology on the backside is what makes these two papers behave so similarly and have such similar texture, ink absorption, and handling properties. Many people cannot tell them apart, so it's not unreasonable to treat them as interchangeable and thus buy depending on price and availability. Right now, I seem to be able to find CiFA baryta at lower price from my suppliers than the IGFS.
Somewhere in the Ilford literature was a statement that IGFS is OBA-free. That's an error. As with CIFA baryta (see above) it has low level of OBAs. However, because the OBA is probably in a subbing layer and/or base sheet, it is more resistant to fade, and the total amount of OBA only substracts visually about 3 points in the b* value (the blue-yellow visual component), so when it does finally burn out it doesn't lead to severe visual differences in the media whitepoint and highlight color as can happen with other papers.
HN Photorag baryta and photo rag pearl both have cotton fiber base sheet. At same gsm weight, cotton generally gives a softer more bendable feel in handling compared to alphacellulose papers. The HN photo rag baryta base sheet also provides a little coarser surface texture (presumably little or no machine roll calendaring) so HN photo rag baryta, like Museo Silver Rag, has a little more noticeable grain direction and surface stipple than Canson Platine Fiber, which in turn has a little more grain direction and stipple compared to CIFA baryta or IGFS. Platine is also a little whiter than HN Photo Rag baryta, both papers achieving their media whitepoint color without any OBA boost. Some people like HN photorag baryta's surface and view it as a somewhat more "natural" aesthetic. Others (like me) prefer a more ordered fine satin or pearl aesthetic which Platine gets a little closer to. Note: if you really desire highly-ordered, grain direction-free finish then RC papers are the way to go.
Harmon Baryta Gloss and Warmtone Baryta papers are the smoothest of the non-RC "traditional fiber papers" I've encountered. They also exhibit less differential gloss and bronzing, IMHO, though none of the gloss/luster type inkjet papers are totally free of these issues, IMHO, when printing with Canon Lucia or Epson Ultrachrome pigmented ink sets. They also use a strong anti-curl technology on the verso similar to IGFA and CIFA Baryta. Seems like the Baryta coated papers may need this extra anti-curl layer on the verso.
Lastly, and I throw this in only as a personal comment that won't affect too many photographers' choices between these papers, In recent months I've started to do backprinting of metadata on my personal work (I don't want to use ink stamps or adhesive labels) To achieve backprinting, the paper doesn't necessarily have to be a dual-sided printable paper, but the back side does have to accept some ink at least as well, for example, as a plain paper. IGFS, and Canson Baryta have the same rather distinct anti-curl layer on the verso which HN photo rag, Platine, Museo Silver Rag, etc. do not have. This layer does not accept the ink well so I was unsuccessful with my goal of back printing on the IGFS and the CIFA baryta, but I did succeed with the "cotton base" papers like Platine and HN Photo Rag Baryta. Again, this back printing issue is not an attribute that the typical user cares about. However, the strong anti-curl layer on the IGFS and CIFA baryta can also give a little trouble with head strikes on printers like the Epson 3880 which don't have vacuum assisted hold down during printing. Many report having to widen the platten gap distance to successfully print on IGFS. What is happening is that the anticurl layer is designed to give exceptional lay-flat characteristics to the finished print, but when high ink loads during printing wet the front side of the paper, the dry anticurl layer on the back is then overcompensating. The paper can then backwards bend towards the print head more than other papers with lesser anti-curl technology. That's why higher platten gap and/or vacuum strengthy may be needed.
All in all, it's great to have so many paper choices. Best advice I can give is take the time to get some real samples and let your own experience/preferences dictate what your favorites will become.