Four criteria:
Reliability
Effectiveness
Cost
Ease of Maintenance
I'd call reliability a wash. Both are pretty solid performers.
For effectiveness, I'd +1 the other posters who've already noted a degree of apples and oranges on that issue. I think I would slightly favor the FAL simply because it has better ergonomics and, if not using some sort of optic, better iron sights.
Cost -- AK wins hands down for the gun. You can get an entry level AK for under $400. You're lucky if you can find an entry level FAL for $600, and at that price you may or may not encounter reliability issues secondary to Century Arms/Hesse/Entreprise or some amateur gunsmith botching the job.
Mags are cheaper for the FAL currently, but AK mags aren't terribly expensive. Ammo favors the 7.62x39 now that surplus supplies of both calibers are drying up.
Ease of Maintenance -- I'd call it a wash, personally.
Hows the handling at CQB ranges with both fullsize and compact models?
The AK beats a full-size FAL in terms of handling. Get a FAL with an 18" or 16" barrel and stack it up against an AK and it's pretty much an even playing field as far as manueverability goes.
For other CQB issues, the AK holds more rounds using standard mags and can hold more rounds than the FAL is one uses non-standard mags (30 rounds for the FAL, 40+ for the AK, etc.).
Downsides -- the AK controls are horribly layed out for a CQB gun (at least in my opinion, and all my combat marksmanship training has been with M4s, so this obviously colors my thinking). The FAL has a safety you can engage and disengage with your firing hand thumb and a charging handle you can operate without taking your firing hand off the pistol grip.
AK safety can barely be finger swiped into fire position if you've got big hands, but even then it's a poor placement and design for CQB shooting. The easy solution is to run you weapon hot all the time, which is also a great recipe for accidental discharges, etc. The charging handle is on the right, meaning you've either got to take your firing hand off the grip or roll the weapon.
Both weapons have magazines you have to rock into place, which is slower in general and harder to accomplish than the straight push into the magwell you have with ARs and some other weapons. Under stress it's much easier to botch a combat reload with an AK, FAL, or other weapon using the same general layout, since it requires a degree of fine motor skills (getting the mag engaged and rocking) rather than the gross movement of finding the magwell and slamming the mag home.
Overall, if you can only get one, I'd say it depends on your budget. If you have, say $600 or less to spend, I'd say go with an AK, and shop around for a nice one. If your budget is $1000 or $1500 or less, I'd vote for a 18" barrel FAL, ideally a Para model.
