mrShrimp:
If I wanted to use built in flash memory, would I get a benefit from buying an newer AVR microcontroller compared to what I already have? (PIC18LF4525-I/P Datasheet Microchip, Download PDF)
You really have to compare individual chips of the two lines to get a meaningful answer.
For example, the Uno uses an ATmega328 and the PIC you linked to is similar in some areas (e.g. operating voltages, resolution of ADC, etc...) and better (maximum clock speed, flash memory capacity, RAM capacity, etc...) in quite a few. On the other hand, the Mega 2560 uses an ATmega2560 which has more total I/O pins, more RAM, much more flash memory, etc... About the only thing that your PIC chip has on the ATmega2560 is raw clock speed (it is possible to run most ATmegas up to 20 MHz, though Arduinos default to 16 MHz). This can make a difference in some applications, but much fewer than you might think.
Of course as mentioned in previous responses all AVR chips, and especially Arduino compatible ones, have one significant advantage over standard PICs; an easier to use programming tool chain. Although I've found PICAXE to be an effective third-party solution for programming PICs, but off-hand I don't know if the PIC you linked to can be used with PICAXE. Even if it could you'd have either buy a new one with the bootloader or put the bootloard on yourself. In any case, I prefer the C/C++ based Arduino IDE compared to either PICAXE's Basic based IDE or having to use assembly.