You're somewhat comparing apples to oranges. I'm not sure you'll find many people proficient in both. I use AutoCAD on a daily basis, and play around with Alibre Xpress.
Alibre is a parametric solid modeler, while AutoCAD is a standard 2D/3D CAD package. AutoCAD 2007 has many more 3D features than it's predecessors, but most of these added features are mainly to speed up the workflow.
Efficiency might depend on what you'll be designing, and would somewhat depend on ones proficiency with either package. Alibre may have an edge due to it's parametric approach to modeling. Making changes in Alibre can be very simple due to the parametrics, while changes in AutoCAD can require major rework.
For someone with no experience with either package, I'd say go with Alibre. An experienced AutoCAD user might find using Alibre a bit frustrating, due to the different workflow.
The CAM program(s) you'll be using may have an influence as well. Simple parts can be made with a quick 2D drawing in AutoCAD and sent to a 2-1/2D CAM program. But assuming you'll always be working with 3D models, again, go with Alibre.