It really depends on what grip you want, I like to use either braided or leather, it feels better than tissue reigns. Leather and Braided reigns look better if you use leather tack so you might want to take that into consideration.
For me personally I feel like I have a lighter grip with leather reign a, so I recommend that for normal training days! If your horse is energetic and non responsive the. braided reigns give me better contact with there mouthes (not that you should hang onto there mouth)
Also if you tend to loose contact braided reigns are good because they don't slip through your hands!
I hope that helped, sorry if there are any spelling mistakes
Rider discipline and preference. If you're vegan, anything leather is out by default. Nylon and beta/biothane are light and easy to care for, but you can't do much of anything to lengthen their lifespan and the lightness can be unfavorable in some applications.
Braided leather reins are pretty and can help with grip depending on how they're made or how worn out they are--they are an enormous hassle to clean properly.
Rubber reins can be nice but can also be bulky and stiff, and they tend to either melt or dry out and crack apart over time. Half-rubber reins I have not seen melt but will eventually crack, they are nicer then full rubber wrapped reins though, personal opinion.
Flat leather reins are fine as long as they're quality and don't have that odd paint like finish on them--that will make you need grippy gloves. I'm partial to flat reins or hand stop reins, whether leather or cotton web.
Cotton web is nice in the summer if you ride without gloves and get sweaty hands. They also make rubberized web reins--not my personal choice but many seem to like them. The rubber eventually flakes away leaving you with the plain web either way.
On the maintenance side personally anything without rubber or being synthetic is best. Keeping leather cared for seems more hassle but they'll last much longer and can generally be repaired(lacing on braided reins tend to break and are a hassle to re-lace, though).
Personally I like a weightier rein these days as the horses will feel you move it much easier than a light weight rein, which helps when trying to keep the signals/aids soft.
I'd say this will depend a lot on what style of riding you do and what's the priority.
I ride Dressage, so my favorite style are leather reins, lined with rubber on the inside, with hand stops They give the best balance of precision and gripiness while still being flexible and adjustable, and the leather exterior gives them, a clean, traditional look.
When I can't use those, leather reins with hand stops are great and get the job done. Hope that helps!
Personally, I use both leather reins and tissue reins. It is up to you, and what you prefer to touch and feel.
If you want to have an opinion more specific, I think leather reins are more suited for dressage and tissue reins for jumping.
But there are many types of reins, for example reins with handles (which makes it possible to have a hand more fixed), braided reins (it's an American style, reins are very flexible and beautiful) or also elastic reins.
I hope this helps!