There are a couple primary factors involved.
1) water boils at a lower temperature at high altitude, meaning it gets boiling fast, but must boil longer to get to the same temperature as if at a lower elevation. That means it take more fuel up high than at a lower elevation to do the same job(unless you like cold meals).
2) cold temperatures, often found with an increase in elevation, can play havok with "canister" fuels systems and can even result in freezing the canister closed after use (as the canisters typically get colder during use - has happened on winter trips to me multiple times). The newer mixed fuel canisters are designed to help overcome this difficulty.
I once made an soda can alcohol stove, and tried it out at a bit over 7K ft. It boiled my water, but really struggled. My buddy made one a couple months ago, that pressurizes quickly - it burns great and efficient even up high, just like my old trusty whisterlite white gas stove. It kind of depends on what you need. I haven't use JetBoil, but heard they they did not get water very hot back in the early JetBoil days. Perhaps that has changed. If not, you may run out of fuel before the boiling water is hot enough to really prepare that 14,000 ft freeze dried meal.
At 8-9.5K I haven't had any altitude related problems with any stove (except my little alcohol stove). Enjoy the trip - sounds like fun!