I've done such comparisons (for the record, I didn't keep the Geek Out either although I'm a big fan of that sort of entrepreneurship) and the AK240 is practically worthless. Money talks and audiophiles listen.
Here's more about my sound setup:
Age: 29
Ears: 26-bit capability
Ear Damage: minimal. I grew up in a rural area, so less traffic/honking/loud concerts...also nobody yelling at the movie screen.
So, just from those cans alone, it made it a pretty easy assessment. I ran both through a Blue line out cable I found at the Dollar Store...The True Blue Magnum X9051's are what they're called (according to the nickname I gave them). The Geek Out across the board was rather vibrant if a little brash when playing louder recordings such as Metal or anything cranked to 11 (I have an amplifier I paid more for in order to achieve that ability). The AK240 sounded toothless and wooden, like I was listening to something being amplified through a Campbell's soup can and then distorted by the wheezings of an 87 year old schizophrenic on his way out of this existence.
Ultimately though, there's worse ways to spend your money than either, such as drugs. Me personally, I'l be sticking with my U2 ipod. It was the most desirable DAP of its time and is desirable again thanks to eBay weirdos wanting a Classic now that they've been canceled because the best-in-industry parts they used were hard to come by.