Technically OLEDB connectivity of an ADP could have a small edge - but the difference between that and your ODBC linked tables should be tiny compared to whether or not you're making well formed requests for data.
An ADP will, at least, force you to think in server querying terms - which is an important habit to get into regardless of the platform you choose.
Linked Tables can leave open the door for sloppy, client side processing requests for the unwary.
(Since you're asking about efficiency I'll not mention the convenience and advantages that Linked Tables can offer - well... OK how about just one - Appending records en masse from local or other linked tables using Jet instead of an iterative process in code or having to perform a server base import.)
So, ultimately, to agree with SQL_Hell, I wouldn't make your decision based on inherent efficiency of the underlying technologies. Make it for a variety of reasons - but always make your requests well formed.