Hi James,
I think they're more alike than different. The differences tend to be related to the drive technology. So where I think the AK bests the K3003 is in timbral decay - a cymbal fades away, it just doesn't stop. Strings on a guitar vibrate after the chord - this is something I'd associate with a single driver, no crossover to worry about. Male vocals are a little more front and center. Sound is a little more cohesive (not that the K3003 isn't...), again all part of that no crossover. Vice versa the K3003 has to my mind a better bass reproduction (capturing that thrum of an acoustic bass better ) - this is part of the dedicated driver approach. It also has a better sense of order when things get loud or complex ie it scales better (albeit not by much but still noticeable) handing off different parts of the spectrum to different drivers helps here. I find these characteristics similar across all sources I own - Cowon P1, AK70, Mojo, Fiio X3ii.
One thing to note is that tip rolling is a whole new world with the AK. Seriously the sound changes more with different tips than any other iem I've heard. It is such that whether you like it or not could depend on the pairing of tips. For me the wrong tips can give either a bass strong (spinfits) or bass weak (comply) emphasis.
Oh and I agree with you on the Vega. I don't know whether they were burned in or not or whether there was an impedance mismatch with the Cowon, but I have never heard an iem where the bass just flat-out dominated everything. Didn't matter the genre - classical - Prokofiev Lt Kije suite, jazz - Miles Davis In a silent Way, EDM - Grimes Art angels, classic pop - Roxy music Avalon - the bass smacked down everything. It was good bass, but... Really struggled to spend a couple of hours auditioning them.
regards,
Giles