What is better(easier) to play after shurgeon castle?
The mines or the boogre's lair?

Don't think it matters in terms of difficulty or order. However, if you have recently converted a character to a new class and are planning on buying training at each level then I would suggest the Stout Mines. Once you are in Boogre pit you have to pretty much finish it before you can go back to town. A new class character may level from 1 to 5 down there. Hope that helps.