I have a cartridge-top stove, a remote-cannister stove with preheat loop, and a meths stove. I've never used a jet boil, a Trangia-type meths stove, or a petrol stove. The one I've use most by a long margin is the cartridge-top item, but that's because I've had it by far the longest (since 1996). I bought it originally for tramping (as they call hiking in the southern hemisphere) and it's good for that because, as everyone's already said, it's small and light. It suffers in the wind – I got a windbreak for it that fits round the top of the cannister – and it's unstable on anything less than a perfectly level surface, which is why there's a small patch of burnt grass surrounded by half-cooked pasta in Napton-on-the-Hill.
So I got the remote cannister one. I reckon it's more efficient, it's definitely more stable, and it's better in the wind because, being lower to the ground, it gets more protection from a windbreak. It's also a bit bulkier, though not much heavier, and I think it was a bit more expensive (I can't remember the price of the cart-top stove back in 1996 but I know I was on a budget!).
The meths (I keep typing methanol then having to delete) stove I've only used once, cos as soon as I got it, this pandemic thing happened. But based on that, it's pretty fast. It's not controllable – it's either burning or not – though it does have a simmer ring, I haven't used it – but you can most definitely blow it out, and easily, no matter how much fuel is in it. You can also store fuel in it. It is tiny and weighs nothing. Being low (right on the ground) it is easy to shield from the wind. Don't yet know what it's like for proper cooking... But another advantage it has is not running out of gas unexpectedly (you can easily see how much meths is left in your bottle) and not having to dispose of a metal cannister.
However, if I were just wanting a roadside brew, as opposed to proper camp cooking, I would and do take a thermos. Especially on an audax where (for me) time is usually tight. But rather than put it in a bottle cage, I'd put in saddlebag (or whatever luggage you have); that way it will stay warm much longer and also won't rattle!