As with all situations, the answer is it depends.
If, for instance, the application runs on a single computer with only one user at a time, Jet will work better and faster.
If the application runs on multiple computers with the backend database on a server and has more than one user at a time, then MSDE can offer significant improvements. Greater improvements are obtained if you use stored procedures or pass-through procedures, because then the work is done at the server, not at each workstation. I have seen a number of applications that were migrated to MSDE but never saw any significant benefit because Jet (which underlies Access) still did all the work locally.
The greatest benefits of MSDE come by modifying the code to take advantage of how MSDE works versus Jet.