I started writing a big post, but ended up deleting all of it. I think the best thing is you to look into the following, read the documents and see the feature list. See which suits you best.
Once I was on a quest to find the best engine for me, but there is not best. All has some strengths and weakness. I am prioritizing them -
Esenthel(No Linux) ,
Leadwerks (No Linux) &
C4 Engine & Torque Game Engine
Havn't evauated yet, 3DGameStudio, DX Studio
Ogre is a rendering engine. To make a game with it you have to work on the additional parts. But, it worth Checking.
i haven't seen mentioned it anywhere, but apart from documentation its great, g3d engine
But, all of it is just a short list of what is available out there. Go here, DevMaster 3d Engine List and see all the engine and their features. Caution : many information are old.
& if you love java, you can always choose jMonkey Engine 3 < I use it :) Its pipeline is shader based.
I havn't checked them in a while. They might have drastic change in their feature set. So check them yourself.