I load both, 45 Colt brass is a little less expensive than 44 WCF and also a little easier to find. I've never had any problems finding 44 WCF except once in a while a supplier will run out.
Some guys complain that 44 WCF is harder to load but I have had no problems with it at all. Starline 44 WCF brass has a little thicker wall than other brands so I have heard claims that Starline is the way to go if you want to avoid the collapsed cases that seem to be the biggest complaint about loading 44 WCF. I also think the ones complaining about loading 44 WCF are trying do it on a progressive press as fast as they can pull the lever.