Gallagher saw his protracted move to Atletico Madrid completed this week, with the former Chelsea midfielder presented to the Atletico fans at the Metropolitano on Thursday.
Asked if he'd take Gallagher or his effective replacement, Dewsbury-Hall - a summer arrival from Leicester City - Sutton told Tribalfootball.com: "Well, it's Gallagher.
"I mean, the fans were singing Conor Gallagher's name yesterday, weren't they? I mean, that's another strange situation. I've got to say, I was surprised that Chelsea have let Gallagher go. (But) I think Dewsbury-Hall is a decent replacement.
"They're not like-for-like players. But this Gallagher thing has been going on for a while now. I think there were rumours in January about him going to Tottenham.
"It's not one of those where he is where, you know, he's Chelsea through and through and they should keep him on because of that. I actually thought he was Chelsea's second best player last season and that's, you know, that's the most important thing.
"I was convinced. He was a real driving force in the middle of the park. We know what Chelsea, are you know, their model and what they're trying to do. But I think that they've lost an excellent player in Conor Gallagher and at this moment in time, I think, you know, most people would say the same.
If you had a straight pick between Gallagher and Dewsbury-Hall, then you'd probably go towards Gallagher. But as I say, they're slightly different players, so that's probably slightly unfair on Dewsbury-Hall."
- Chris Sutton was speaking to Tribalfootball on behalf of Best Online Poker Sites