First up - I own the E620 but can only go on web reviews as far as the K-x is concerned.
Both got the top 'Highly Recommended' rating from DPReview - there can be little doubt that both are very capable cameras.
Pros of the E-620 (vs K-x): multi-angle screen, lighter weight (and lighter lenses), shows active focus points in the viewfinder, Longer exposures allowed (60s as opposed to 30s), better IS (according to DPR tests).
Pros of the K-x (vs E-620): better low-light performance, faster exposures allowed (1/6000s as opposed to 1/4000s), faster continuous shooting (4.7 fps vs 4).
Other significant differences:
The E620 has a proprietary battery (CIPA rated at 500 shots, although I got 1255 out of a single charge in Washington last week), while the K-x takes AA batteries. These are widely available, but do not tend to last as long (I've found that rechargeable AAs need replacing around once a year at least - although they are improving).
The E620 can be used with a battery grip, not an option for the K-x.
The E620 is generally a more customizable camera (which might be a good or bad thing!)
Had a written this a few months back, I'd have commented that Pentax has not got a good reputation for out-of-camera JPEGs, while Olympus has one of the best JPEG engines going. With the K-x, Pentax seem to have finally sorted this out, however, and their JPEGs are now at a similar level to everyone elses.
Overall - I prefer the E620 for general photography (obviously, as that's what I bought), but the K-x is probably better for very low-light or other high-ISO applications (shooting fast sports, for instance). If that's what you're likely to be shooting, then you'd be better off with the K-x. There's no way I could live with not knowing which AF point the camera had selected - so the K-x would never be my choice.