The one you already have is always better if you want to start now, since you don't have to wait for a new development board to arrive.

If you plan a commercial project, then availability and price is probably the most important aspects. And that's something for you to look into.

If you want extremely low power consumption, you might look into the PIC nanoWatt-series chips.

If you want extreme expandability into high-end, it's the ARM chips you should look at. No bank-switching of memory which is a big problem with 8051 chips, and good support for function pointers. And the sky is the limit when it comes to availability of peripherials integrated in the processors. The number of different ARM chips released is exploding, but that doesn't mean other architectures will continue to be very good to use. It's all a question of needs.

If giving importance to already known skills, you should stay with 8051. You have the development tools, and the purchase channels. And you can reuse code from previous projects.

Right now, I can't find a reason for moving to AVR chips, unless you want to duplicate any existing project that is AVR-based, allowing you to use already existing source code.

You never switch processor unless you have specific reasons. But if the reasons are strong enough, you might switch processor for each and every project, just to get the "optimal" processor for that specific project.

You haven't given us any facts to work on, so we can't really help you with suggestions.