From what I know, on higher level, two VMs are actually quite similar: both are classic stack-based machines, with largely high-level operations (e.g. virtual method dispatch is an opcode). That said, CLR lets you get down to the metal if you want, as it has raw data pointers with arithmetic, raw function pointers, unions etc. It also has proper tailcalls. So, if the implementation of language needs any of the above (e.g. Scheme spec mandates tailcalls), or if it is significantly advantaged by having those features, then you would probably want to go the CLR way.
The other advantage there is that you get a stock API to emit bytecode there - System.Reflection.Emit
- even though it is somewhat limited for full-fledged compiler scenarios, it is still generally enough for a simple compiler.
With JVM, two main advantages you get are better portability, and the fact that bytecode itself is arguably simpler (because of less features).