Like most things, the truth lies somewhere in the middle. Conor can't make featherweight with all of his abilities intact anymore, while Cowboy isn't an elite welterweight.
That said, Conor is nothing more than a blown up lightweight with zero added nuances as a welterweight. This is evidenced in his struggles with Nate. While Cowboy, at least in the past, has had legitimate business at that weight. This is evidenced by his close fight with Lawler which could have gone either way, and his close but clear loss to Leon Edwards.
I believe Conor's speed and cardio is worse at a higher weight. I also believe Cowboy takes a better shot, both to the body and the head, at a higher weight. Conor still might beat him though, because stylistic problems are a motherfucker.