How does the Arduino compare to PIC and AVR for serious learners
Unless you are on an extremely tight budget (like saving-pocket-money levels), then I wouldn't sweat the decision of which to try first too much. Just pick one, and expect that once you've started you will try others.

IMHO you can't really go wrong with an Arduino as a first choice:


Precisely because of its popularity and its purported simplicity (when compared to PIC) you will find a wealth of information and support on the net
And with the standard IDE you can pretty much bank on an encouraging first experience as you actually get to make it do stuff (compared with going straight to an AVR chip).


So it is unlikely you will fall at the first hurdle and be disenchanted and frustrated as a result. 

Do not worry too much about getting stuck in a black box that prevents you learning to deeper levels. But the onus will be on you to push beyond the basics e.g.:


as kyranf suggests, once you are comfortable you can throw away the standard IDE and try Atmel Studio instead
or you can start hacking the IDE and libraries available here
write your own libraries in C/C++
eschew the board and stick an AVR on a breadboard and provide support circuits yourself (it helps that the board design is open sourced).


About the only downside of starting with an Arduino I can think of is having to suffer the occasional disparaging remarks and trolling by Real™ Engineers! Kind of like programmers admitting their first language was BASIC;-)