That savage 110/10, 11/111, 12/112 and the 16/116 are all better build quality than the axis. 110 (means long action) 10(means short action.) and so for with the other model numbers. The axis is generally an entry level rifle but they are inherently accurate, but lacking in fit and finish as compared to the other savage models listed above.
Note: all axis rifles are built off a long action that will create a longer bolt throw even in short action calls like .243 and .308 not a big deal but just saying.
I suggest you head to the gun shop and fondle all of them. The differences will quickly become apparent. As for twist rates you have to look at the bullets weight you will mainly shoot to decide on which is most versitle for you. Many will say savages are ugly but once you see the beautiful groups on your target they are a supermodel.
If it were me, of your choices I'd get the international trophy version in one of the models listed above. And I'd stick to the standard sportier barrel an stay away from the medium contour (predator versions) they are just heavy to carry IMO