First, I agree with almost everything that others have said about the Whisperlite. I still love that stove - it saw me through some pretty difficult conditions. The only problem I ever had was once the pump mysteriously stopped pressurizing the fuel bottle. Something in there was clogged - I still don't know how, to this day. I think it might actually have been a result of some water getting in there maybe even from freezing fog. Fortunately, my partner that time had a spare.
I guess the one thing I'd disagree on is the energy content: should be about the same for white gas and isobutane/propane. I don't carry any more isobutane than I did white gas. Same weight, roughly same bulk.
There is no perfect, idiot-proof stove for winter use. But net-net, I like the Reactor a little bit more. In my hands, it does what I want it to do quite a bit easier, quite a bit faster, and with significantly less risk of catastrophic failure.
Here is how I'd characterize the user experience for each stove:
1. Start up
Whisperlite - take stove and fuel bottle out, attach pump to fuel bottle and pump to pressurize (hope your o-rings are ok), unfold legs of stove, attach to fuel bottle, position somewhere relatively flat. If in snow, you should have carried a base of some kind to put the stove on. Unfold windscreen. Carefully fill priming cup half way (hope fuel comes out when you open valve). Light priming cup, place windscreen around stove. Observe carefully. If you're in a tent vestibule, be VERY VERY careful. This part is, like, seriously sketchy in windy, spin-drifty, cramped vestibules. When flame dies down to the perfect size, crack valve until you see a blue flame. Be VERY cognizant of potential flare ups. If you get a blue flame, you're now in a happy space and can go about your business melting snow like a boss.
Reactor - attach stove to fuel canister, place the whole rig in a small bowl of liquid water, light. This is trivial in almost any conditions. You're now in a happy space. Melt snow like a boss.
Obvious question: where do I get some liquid water? A: you saved a couple ounces in your water bottle. Q2: What if I don't have ANY liquid water because I forgot or it all froze? A2: you'll almost certainly still be able to light the Reactor, it'll just run VERY slowly. Melt a little bit of snow, which will only take a couple of minutes. Now you've got your liquid water.
2. Running the stoves
Whisperlite - very straight forward. Just keep her going. You'll need to pump the bottle occasionally to keep the bottle pressurized. Easy. Relax as you drink your soup with the soothing hiss in the background.
Reactor - every couple of liters, you'll need to replenish your liquid water bath. Just dump it out (or back into your pot), put a couple ounces of warm (not boiling) water back in the bowl, continue. Easy. This is all somewhat less relaxing because the Reactor is so freakishly fast that you'll be constantly filling Nalgenes and getting more snow.
3. Finishing up
Whisperlite - Turn fuel valve off. Blow out flame. Try not to be nauseated as white gas vapors assault your lungs and sinuses.
Reactor - Turn it off.
Other odds and ends: the two stoves weigh roughly the same after everything. The Reactor uses a lot less fuel in my hands and boils water much faster. The reactor is easier to start in difficult conditions and much easier to use in a vestibule. The Reactor is much less prone to serious problems, such as a clogged fuel line, broken pump, or leaking o-rings. It is easy (and doesn't weigh very much) to carry a spare Reactor stove top. You don't need an extra fuel canister, pot, or water bowl. So you can have redundancy in this critical item with little weight penalty.
The only hack you need with the Reactor is to bring a small bowl with you to serve as a water bath. I've used it in pretty heavy wind with spindrift blowing into my vestibule at about 10 below zero. This was in the col between Madison and Adams. Actually, for that trip, I had both stoves with me as I was still feeling out what conditions I could use the Reactor in. I first tried to get my Whisperlite started, feeling that it was the more reliable choice in the given condtions, but snow was blowing onto the burner as I was getting it set up, and the priming cup was also filling with snow. It was bad. I was worried the fuel would mix with the snow and create higher probability of flare up, which would not be good in my vestibule. I was actually a little bit gripped right then and there. I set it aside, pulled out my Reactor, and had it going within 30 seconds. It still was not easy - I was trying to get the vestibule sealed up enough that the spindrift would stay out, while also keeping water production going. The wind was just plain nasty. We were flogging ourselves continuously for trying to save the 30 minutes it would have taken us to find a more sheltered spot below treeline. Dumb. But yeah. I'm mighty glad we had the Reactor.
I haven't used a Jetboil, but I think it is not as resistant to wind, it is a little bit more tippy, and the push button igniter can be a bit problematic if you're in freezing fog or other difficult conditions. You still need a water bath to keep the canister warm, but everything works a little bit less good than the Reactor, I think. The requisite hacks seem a bit more problematic.
Using a foil wind screen with a canister stove is scary to me.
Sorry for the novel.