If you use small Jazz III style picks and happy with them most of the time, but it doesn't feel quite right when used for rhythm picking and chord strumming. If that describes you, you need to try one of the Dunlop Tortex TIII picks. My personal favorite is the 1.0mm (blue) version of the Tortex TIII, but it comes in 0.5, 0.6, 0.73, 0.88, 1.0, 1.14, 1.35 and 1.5 millimetre versions.
Why Tortex TIII?
I used to carry a standard size Tortex 1.4mm pick, for songs where the Jazz III didn't really work for me, primarily for picking precision and control reasons, but since switching picks in the middle of a song is not something I'm willing to do, I was never happy with either pick I had. The Tortex TIII combines the comfortable size of the more "standard" sized Tortex picks with the sharp tip of Jazz III style picks. The bigger size allows you to alter the length of the pick to your needs while you play, and maintain better grip while strumming, and the sharp tip provides more picking accuracy and speed for solos, fast riffs and staccatos.
Material
As far as sound goes, the material from which Tortex picks are made provides brighter, more aggressive attack, which is a matter of taste. Jazz IIIs are typically darker (I would guess that's why they are called "Jazz") compared to Tortex. So if you like the sound and attack of a Jazz III better but find it too small, try the large version of the Jazz III, I believe they call it Jazz III XL, which has the same shape and material, only larger.
A pick is really one of those little cheap accessories that can make a really huge difference - no kidding here. It's a matter of personal taste and physiology, but you'll never know until you try, and since trying a new pick every now and then is no big deal for anyone, I highly recommend it to any guitar player.
More Alternatives
If you find the TIII too long and cumbersome, try the Tortex Flow. The Flow is closer to the Jazz III XL in shape and provides all the qualities of the Tortex family of course. If the Jazz III XL has the perfect shape for you, but you want the attack of the Tortex material, try the Tortex Jazz III XL.