Replacing toaster oven with convection oven or convection microwave?
Please correct me if I'm wrong, but if I've read your question correctly, you already have a toaster oven with a convection function and are considering options for replacing it. If that's the case, you know how convection cooking fits into your lifestyle, and when and why you like to use it. 

Hopefully I can help with one part of your question! We recently bought a new regular oven and a new toaster oven, both with convection options. The convection functions work exactly the same way and serve the same purpose, which is primarily to cook food more quickly and evenly. My oven takes longer to pre-heat, which makes sense because it's bigger, but that's the only major difference. The actual cooking time doesn't vary, even though I originally thought it would. I use each appliance at different times depending on various factors, but I cook the same foods in both, and the end result is very much the same.  

I don't have any experience with convection microwaves, so I'm sorry but I can't help you there.