@RyanS Thanks for reaching out!
We also appreciate the clarity of exactly what you're looking for in a stove. I've used canister, liquid fuel, wood burning, and alcohol stoves in my outdoor adventures and they have all worked well. I have only ever owned canister stoves, however, and they haven't let me down yet! It is really hard to beat the weight and ease of use of a canister stove. I've taken the MSR Reactor Stove System to altitude and I can vouch for it's performance at 10,000'. If you do choose a canister stove that you plan on using consistently at altitude or in cold weather, make sure it has a regulator built in (like the Jetboil Sumo Cooking system) or allows you to use the canister upside down (cold weather and altitude lower the pressure in the canister and the gas sinks to the bottom of the canister). Currently, I have a MSR Windburner DUO Stove System that I really enjoy for its size and packability.
Because you have better control of the pressure with a liquid fuel stove (you can not only adjust the valve on the fuel bottle, but also how much pressure you put in the bottle as well), the main advantages are flame control (for simmering and cooking), cold temperature performance, and working at altitude. Because the fuel becomes a vapor by passing over the flame of the stove itself, rather than requiring a pressurized canister to keep the fuel vaporized, liquid fuel stoves are much more versatile in varying conditions. That being said, they are heavier and require pumping and priming the stove.
One great option to help make this decision easier is the MSR WhisperLite Universal Backpacking Stove. It can use both liquid fuel and canister fuel, plus the canister sits inverted in case you need some help in cold temps or at altitude. You will pay a few ounces of a weight penalty with this stove, but if it checks off all of your needs it could be a great option.
Hopefully this helps, thanks!