Biggest issue with DCL is his injury record. I do think he would do better under Moyes than Dyche. He is by far our best striker at the moment. He has everything you'd want from a number nine except the most important, goalscoring ability. I don't think he will ever be great at that but he's really good at link-up play, he can actually trap the ball and pass to a teammate. He's one of the best strikers in the league with his head. He's pretty smart, makes more correct choices than most strikers. He's relatively quick, not a speed merchant but can beat defenders with pace.
Unfortunately his finishing, especially in one-on-ones is rubbish. Not the first striker who is a decent finisher as long as he doesn't have to think about finishing. The more time he has to think what to do the more likely he'll make a mess out of it. And of course his fitness record is poor. I would imagine other clubs have been looking at that as well and interest has twindled.
His good spell under Ancelotti wasn't because he was suddenly all-around much better. He just finished his chances and he was fit. Part of the issue with his finishing could also be under Dyche that a striker in Dyche's team doesn't get many chances in a match so the pressure to score from one of them is high. Getting more chances could ease that. But I don't if anything can be done with his fitness record. He has had lots of hamstring issues and I have no idea if that can even be helped.