I don't have much (not really any) experience in this area, so you might want to verify some of the following for yourself (or maybe someone else can correct me where necessary?).
The two languages I work with most nowadays are C# and Java, so I am naturally inclined to their methodologies. As most people know, both are compiled to byte code, and both platforms (the CLR and the JVM) utilize JIT (at least in the mainstream implementations). Also, I would guess that the jitters for each platform are written in C/C++, but I really don't know for sure.
All-in-all, these languages and their respective platforms are pretty similar to your situation (aside from the dynamic part, but I'm not sure if this matters). Also, since they are such mainstream languages, I'm sure their implementations can serve as a pretty good guide for your design.
With that out of the way, I know for sure that both the CLR and the JVM are stack-based architectures. Some of the advantages which I remember for stack-based vs register-based are
- Smaller generated code
- Simpler interpreters
- Simpler compilers
- etc.
Also, I find stack-based to be a little more intuitive and readable, but that's a subjective thing, and like I said before, I haven't seen too much byte code yet.
Some advantages of the register-based architecture are
- Less instructions must be executed
- Faster interpreters (follows from #1)
- Can more readily be translated to machine code, since most commonplace hardwares are register based
- etc.
Of course, there are always ways to offset the disadvantages for each, but I think these describe the obvious things to consider.