I have both leathers (Helimot custom suit) and textile (Motoport Ultra II Cordura) gear. Here're some Pros and Cons of each:
Leathers are hot in the summer and cold in the winter. The right textile suit can be cool in the summer and warm in the winter. My Motoport gear isn't Gore-Tex lined, which means it is very cool in the summer, but not rainproof/warm in the winter.
Both types of materials will protect you in a crash, assuming your gear is reasonably well-made. The main difference seems to be the amount of damage the suit will take. With leathers, the suit will likely sustain minimal damage and be ready to go as soon as you are. Textiles, on the other hand, tend to sacrifice themselves in the process of protecting you. That isn't to say your textile suit will be destroyed, just that it will probably need repairs after a crash.
The material your suit is designed with primarily protects you from slides. For impact protection, you need body armor. Obviously, you can get armor of varying qualities in both leather and textile garments. FWIW, I'm completely sold (in an ass-meets-concrete-at-70mph sort of way) on the soft armor in my Helimot suit.
One negative I've heard about textiles is that many of them are made with Nylon or polyurethane coatings, which can melt to your skin during a long, high-speed slide. I, personally, have seen several people crash while wearing textile gear and this didn't happen to them. I also haven't heard anyone say "Yeah, that happened to me!", so I have no idea how likely this is.
I find that it's easier to grip the tank on my bike when wearing leathers. My textile pants feel slippery against the tank, which saps my confidence during hard braking or hanging off. Having some sort of tank bra (I always use Second Look) helps with this.
Textile gear is more likely to fit over your street clothes than leathers. This makes textile gear great for commuting. You can find leathers designed to fit over clothes, but most of the leather gear isn't.
Textile gear tends to have better rain protection than leathers. This isn't to say you'll get sopping wet if you ride in the rain in leathers, but in most cases the zippers on leather garments aren't protected and will leak. It's also not to say that textile gear offers perfect protection from the elements! You may need to seal the seams, zippers, etc. if you don't want them to leak through on a long ride. If you buy leathers and plan to ride in the rain, you can always get some lightweight rain gear to wear over the leathers.
Price, as far as I can tell, is similar between the two materials. You can certainly find some cheap-ass textile gear, but for the good stuff (e.g. Aerostich) you have to spend a decent amount of money. You can buy-off-the-rack leather suits for about the same price as an Aerostich. Of course, if you want a Dainese suit or a custom leather suit, you're going to spend a lot more money.