Extensive, massive discussions all over the Sony forum and all over the internet. Now, comparing the Sony DSLR A580 to the SLT A55:
In summary:
DSLT has:
1. No mirror slap (both the vibrations and the noise)
2. faster FPS as the mirror does not need to be lifted out of the way
3. The ability to continuously autofocus using faster phase detect in video as well as live view
4. The A55 also has built-in GPS
5. An EVF that can immediately show you the effects of aperture, whitebalance, etc changes as well as tilt/level horizon
DSLR has:
1. An OVF
2. Erm. That's mainly it - aside form that, the A55 and A580 are similar in terms of fast AF in live view, built-in SSS, articulating LCD, etc.