There are few debates in the jiu jitsu world more heated and polarizing than that of gi pant material preference. I mean, we've seen jiu jitsu players nearly come to blows over it!
Well, not really... but in all seriousness, an individual's preferences on the material of gi pants does tend to be very particular. There are few bjj players in the community who don't care either way; people either prefer cotton, or prefer ripstop.
So what's the difference? We'll tell you:
Cotton is the most traditional material for jiu jitsu gi pants... and really for all kinds of martial arts kimonos, as cotton fabric manufacture has been around for thousands of years. In the Brazilian jiu jitsu gi market, two different kinds of cotton fabrics dominate: twill and duck. Much like in gi jackets, those two terms refer to the weave. Duck (sometimes called "canvas") has a standard square basket weave, and twill (of which "drill" is a variation) has a more diagonal weave. Because these fabrics are made from 100% cotton, they will shrink, depending on how you wash and dry them. This is because the cotton fibers are stretched during weaving, and when heat is applied, they retract to a more natural state.
Ripstop was developed during WWII for the manufacture of parachutes, replacing silk, which was much more costly. It soon became a material of choice for military uniforms, camping gear, sporting equipment, and... Brazilian jiu jitsu uniforms. The ripstop made for jiu jitsu gis are often made from a polyester/cotton blend, with stronger reinforcement fibers woven in a cross-hatch pattern throughout, giving ripstop its distinctive look. Because of the synthetic makeup of the fabric, ripstop tends to shrink less - and sometimes not at all, depending on the cotton-to-polyester ratio of the fabric. As its name suggests, it is also a very durable fabric, highly resistant to tearing.
The preference for cotton versus ripstop jiu jitsu pants really comes down to feel and performance during grappling. Cotton is a much softer fabric, and has a bit of stretch, especially when wet (with sweat, of course). Because jiu jitsu involves a lot of contortions of the body, unrestricted range of motion is key, so some practitioners like to have a bit of stretch in their pants. Ripstop doesn't have as much give, and tends to be a bit stiffer, which can be an issue, depending on how tight you like to wear your pants. However, ripstop also tends to be harder to grip, which is why a lot of competitors prefer ripstop pants.
The best way to determine your preference is try them both. The old adage "If you never try, you'll never know" applies to both your jiu jitsu practice, as well as your jiu jitsu gi pants.
Train on. Oss.