Vinyl: Vinyl is the thinnest material, weighing in at 18 oz. fabric weight, and usually associated with earlier Wranglers like the YJ. Vinyl, as you might expect, has a plastic feel to it with a glossy appearance when cleaned. The underside of the top is a thin cloth layer. If you're after a classic off-roader look while not minding a bit of extra road and wind noise, a vinyl top will do just fine. Vinyl is generally weather and UV resistant while being an easy to clean option.
Denim: Denim is how it sounds, but don't worry. You won't be putting a pair of jeans on your Jeep. Denim tops have a vinyl coating for weather resistance, otherwise you'd be swimming in mildew. Beneath the coating, is your denim material, a polyester/cotton hybrid. Aftermarket denim tops are usually thicker than their vinyl cousins, weighing in between 18-23 oz. Generally, OEM replacement denim tops will err on the 18 oz. side. Do yourself a favor and reach for the sturdier aftermarket options. Denim tops are ideal for those looking to maintain a factory appearance but want a quieter ride.
Sailcloth: FCA introduced sailcloth tops midway through the TJ line in 2001. These tops usually weigh in around 28 oz., making them substantially quieter than denim and vinyl. Sailcloth tops have three layers to them, two vinyl layers to boost weather and UV resistance over the previous two top options, and the interior layer is the polyester/cotton weave. These extra layers do mean a higher cost. Something to keep in mind if you're not after that all-weather protection in favor of sunny topless days.
Twill: Arguably the best of the four, twill is most certainly the thickest at 30 oz. Twill is the material used for luxury sedans and the like, so you can expect the quietest ride with this type of top. This is the top of choice for daily driven Jeeps as it provides the best insulation from weather as well as noise. The secondary selling point of twill is its flexibility. With twill, you won't have to deal with the characteristic creases and tears with more rigid, vinyl based tops. With all of these perks, expect a high price point.