Charcoal because exchanging the gas canister and everything is too much work to be honest. I'd much rather just grab a bag of charcoal at the store and throw it on the grill and call it a day versus uninstalling it, taking it in, exchanging it, taking it back, plugging it all back in, and then going to work. The less steps the better.
I have used all manners of grills from giant 8-foot gas grills to cooking whole pigs over wood and at home, I use a basic weber (with the side table).
With good charcoal and a chimney starter, you can have it super hot in a matter of minutes. The grill gets hotter, it's almost maintenance-free and the flavour of the food is superior. I cook pizzas on a stone right in my grill.
We have a propane grill that is hooked up to our huge propane tank under the ground. I like it because it's easy to just switch on and it heats up immediately.
My mom used to prefer the charcoal grills for the flavor. I didn't really care for it myself.