Hi John and Everyone,
I like AVRs but I am looking at ARMs as well now. I don't like PICs for aesthetic reasons but I didn't like 5051s either and I have used them a lot.
PICAXEs are not just limited by the chip resources. They are programmed in PICAXE BASIC which is ssllooooww. This also uses a lot of the resources so there are serious overheads. The BASIC is probably the biggest limitation. PICONE manages it O.K. but does use two of the larger chips. A maze solver using an 08M would be a challenge.
There is a thriving PICAXE community and software tricks are quickly passed around. Once someone has a solution to making a solver with this level of resourcing, it would be necessary to redefine the challenge. It's a bit like the classic maths problems. For example, once someone has solved the map colouring problem it became uninteresting. The problem must be nearly soluble but not quite!