Only looking at core differences that caught my eye:
ThinApp (now - as of latest version 4.7) does not support native x64 applications. It does support x86 applications running on x64 platform through WoW64. Source - (vendor has done a lot of homework hiding this, it's very easy to miss) - Official User Guide, Certain operating systems and applications are not supported by ThinApp.
ThinApp integrates a licensing date stamp inside each package. BEFORE the license runs out, you have to update each application package and re-roll it to your clients. Source - 1, 2.
Virtualizing applications results in SLOWER performance (responsiveness, launch times , read - think about the real impact on user experience!) and quotes from a superb study by Login Consultants Application Virtualization Impact on VDI:
"Conclusion on Microsoft App-V: When App-V is fully pre-cached, Winword starts 20% slower compared to locally installed application."
"Conclusion on VMware ThinApp: The initial launch of Winword using ThinApp streamed is around 40% slower than locally installed."
"Conclusion: App-V and ThinApp are between 140% and 170% slower compared to local when it comes to this communication with the local system."
From my personal experience - multiple customers failed to adapt a working VDI environments because the end-user feedback during a pilot is "Slow, slow, slow".
App-V does not support virtualizing IE (a valid points for customers looking for IE6 compatibility solution).
Some extras - A common misconception is that Application Virtualization helps you solve Application Compatibility issues on Windows Vista/7/8 - it does not. It helps you solve Application Interoperability and Conflicts.