Well, the Axis is an Axis, and the 111 is a 111!

111s are built on the 110 pattern and have the benefit of an Accutrigger and a rather sizable aftermarket. The Axis is a completely different rifle, though there are some external and internal similarities. Differences from the 110 included the fact that Axises are all built on the same long action receiver, irrespective of whether they are chambered in .223 Rem or .30-06. The receiver is also a closed top design similar to but entirely distinct from the Target actions. Axises' recoil lugs are also embedded in the stocks rather than attached to the barrel shank. The bolt handle and body and firing pin are also different from the 110.

However, the bolt head and its parts are interchangeable with short action (10) bolt heads. Small shank barrels from the 10/110 rifles also interchange with the Axis barrel. The trigger system is similar to late Stevens 200s and some pre-Accutrigger 10/110 rifles. Axis magazines are also the same as 10/110 rifles that use plastic floorplates. While one-piece scope mounts for the Axis and 110 will not interchange, any two-piece scope mount for round back 10/100 rifles will work with the Axis.

If you can get them for the same price, my suggestion would be the 111. The Trophy Hunter line is the cheapest of Savage's main marque (it uses the same plastic floorplate magazines as the Axis, I believe), but it does have the Accutrigger, which is a step above the Axis' factory trigger, and it is more upgradable down the road with the least amount of effort or expenditure.