I'm big into tens, and I've been considering an EAA in that calibre, but I'd probably go for a higher end one. I think you can change calibres in that platform, so if that is true and it is tough enough for the 10mm, I bet it is overbuilt for the other calibres --not a bad thing at all for a range pistol. The ones I've felt seemed pretty nice for the price. I haven't felt an Elite yet, and if I get one it will have to have a great trigger. It'll also have to be pretty beefy for the 10mm.
I also have a G20, a G29, and a Smith 1006 in 10mm. Those are all great, I consider them to be the best of the current production 10mm's. Best thing is they are all decently priced and built well. The 1006 is a tank, capable of handling serious loads. The G20 is a high cap beast. The G29 is a great carry piece.
The Witness? I bet it would be a great range pistol IF it has a great trigger. Otherwise, I'd go with one of the other three. The 1911 10mm's will probably have the best triggers, but they also have the thinnest chamber walls too, the G20 and G29 in the middle, and the 1006 the thickest. Not sure where the EAA falls in here. But chamber wall thickness is important with the heavy loads.