I've been working on an adp FE to a SQL Server BE for a while now. Here's my take on it:
The one slight advantage to ADPs that I can see is that they don't use an external ODBC connection, which could be used by other 'applications' without you wanting them to: Anyone can create an access database and connect to that DSN and link the tables and bypass your FE.
Certainly, the connection details can be read out of an ADP but it's a little less obvious and with some clever code it could be made harder (having no connection at startup, setting it after startup and disconnecting again before close - although if it crashes or it's killed then the connection info will remain in it).
Either way, that is the main problem with an Access FE - the security: the connection string to the Server will always be accessible one way or another and thus the FE can be bypassed and the tables accessed directly (unless there's some clever code on the FE and the Server that will disconnect a connection if it doesn't do something very specific - i.e. execute an SP with a particular password - very soon after connecting). On top of that it's some work to make sure a user can never get into the Access Options and change settings.
The second biggest problem is it's always a little bit unprofessional and hiding Access quirks from end users to keep up a professional appearance is very tricky.
For best results, especially with regards to security and professional appearance then a better FE is needed. The downside is it's a lot more work. Even all the work it takes to lock down an Access FE as best you can and make it look as professional as possible (capture and replace all Access error messages for instance) is less work than building the same thing in VB.NET.
If it's going to be a web interface and therefore accessible to all the hackers in the world then Access is not nearly secure enough imo.
Still, ADPs seem a little bit more secure than odbc connected DBs to me because of the internalized connection settings, which is also useful for deployment - you just have to deploy the adp, not a file DSN too or setting up a Machine DSN on each client. (Having said that, having an external DSN that can be edited easily has its own advantages when deploying to environments where the connection string needs to change.)
But as Nellie said, whether to use access depends on a lot of factors, but I think security is the biggest and most deciding factor. If that's not so much a concern (and a slightly less than perfect finish is ok) then Access is a good FE and because ADPs are deprecated you're better off choosing the ODBC method.