Having seen and enjoyed both I would say different, not better.
Shaun the Sheep takes a more relaxed approach to telling the story. The Minions crams in a lot of story in a short time and it pretty frenetic. I bought Shaun the Sheep on blu ray from the UK a couple of months before it was released in the UK and have watched it a few times, enjoying it more each time. I've seen the Minions a couple of times in the cinema now and enjoyed it more second time around.
I would say both are better than Disney's recent output.
Agree. On another note, even if you don't like Inside Out at least you can acknowledge that they aimed at making a film that anyone can enjoy, instead of just brainwashed toddlers like Minions.