I have both, a propane camp stove and an alcohol stove.
I see no real difference, both produce fumes.
If I am going to be using either one for cooking I arrange for some kind of ventilation.
Cheapest would be one or more 12v fans scavenged from discarded computers, set on a window sill.
That's what I use.
A carbon monoxide alarm would be a really, really good idea, too.