In August 2011 the SQL Server client team published a blog post entitled Microsoft is Aligning with ODBC for Native Relational Data Access in which they basically said "OLE DB is the past, ODBC is the future. Deal with it.". From that blog post:

We encourage you to adopt ODBC in the development of your new and future versions of your application. You don’t need to change your existing applications using OLE DB, as they will continue to be supported on Denali throughout its lifecycle. While this gives you a large window of opportunity for changing your applications before the deprecation goes into effect, you may want to consider migrating those applications to ODBC as a part of your future roadmap.

I recently undertook a project using SSIS2012 and heeded that advice by opting to use ODBC Connection Managers rather than OLE DB Connection Managers. Unfortunately my finding was that the ODBC Connection Manager is not yet ready for primetime use in SSIS 2012. The main issue I found was that you can't populate an Object variable with a recordset when using an Execute SQL Task connecting to an ODBC data source; any attempt to do so will result in an error:

"Disconnected recordsets are not available from ODBC connections."

I have filed a bug on Connect at ODBC Connection Manager does not have same funcitonality as OLE DB. For this reason I strongly recommend that you don't make the move to ODBC Connection Managers in SSIS just yet - best to wait for the next version of SSIS before doing that.

I found another couple of issues with the ODBC Connection Manager that are worth keeping in mind:

• It doesn't recognise System Data Source Names (DSNs), only User DSNs (bug filed at ODBC System DSNs are not available in the ODBC Connection Manager)  UPDATE: According to a comment on that Connect item this may only be a problem on 64bit.
  
• In the OLE DB Connection Manager parameter ordinals are 0-based, in the ODBC Connection Manager they are 1-based (oh I just can't wait for the upgrade mess that ensues from this one!!!)

You have been warned!

@jamiet