The AVR is a pretty typical Harvard RISC: 32 registers, memory load/store, direct/indirect jumps, stack pointer pointing at ram, etc. It's still 8/16 bit, so some pairs of 8 bit registers work like 16 bit registers.
The PIC has one accumulator register; ram is a set of (manually selected) register banks. Instructions operate on the accumulator and an operand in the selected bank. The stack is totally separate from other RAM, so it's fixed size (8 maybe?) and can only be used with call/return.
I don't want to be judgmental; there's certainly some strange virtues to PIC, like the lack of any real state to save/restore on ISR entry/exit; but they really just don't fit my mental concept of a CPU.
Exercise for the reader: Given the stack and register bank selection, which one of these has better C compilers?
(Still, if you're learning something new, gamble is right: ARM is the future.)