In a way, you're talking about different classes of stoves. The Tilite is a stove that an ultralighter might carry. The Jetboil is a stove that a "traditional" backpacker might carry. In other words, the Jetboil is a heavier stove and is a stove that most people on this site would have no interest in.
In your case, where wind is an issue, the Tilite might not work well even though it's a great choice in terms of weight. It might be worth it to carry the Jetboil since, as you mentioned, it does have some wind resistance.
An MSR Reactor, which is even heavier that the Jetboil, offers even more wind resistance, but, as I say, it's quite heavy and also quite expensive. You'd have to decide how much weight you're willing to carry and how much cash you'd be willing to part with.
There are other choices that would be wind resistant, like a remote canister stove. The stoves above are all top mounted canister stoves (where the stove just screws into the canister). With a remote canister stove, the stove has legs and sits on the ground, and the canister is placed some distance from the stove. A remote canister set up allows one to use a full windscreen without risk of heating the canister (and thereby risking an explosion). An example of a remote canister stove would be the MSR Windpro whose very name describes its intended niche.
You could also use something like a full Trangia alcohol stove or a remote tank "white gas" type stove, both of which tend to do well in the wind. Both, however, tend to be heavy.
Hope that helps,
HJ