I will probably dive way to far into this as i am an archery nut but here we go:
Cable driven:
Pro - if installed correctly is almost fail safe. the cable will always pull the forks up but drops with a spring (con) when released
- most common between the two as far as everyone having one
Cons - if fails or not installed correctly, takes a press to correct
- installation takes some basic knowledge and if you have a draw board, can fine tune to come up and stay up for a shorter or longer amount of time in the release process (A pro if you have someone that knows what they are doing)
Limb driven:
Pro - simple to install (tie to your limb, tie to rest, go hunt)
-is held up by a spring (con), drops with the limb extension
- stays up longer in the shot cycle...can be a con if you have bad form or jerk
- repair is simple if fail, retie to whatever fails and a shoe string can work in a pinch...believe me
Con - not as common and more expensive (typically)
- extra cable exposed in the bow that can get in the way of sight bars or possibly catch on limbs/sticks
- may have to be creative on how to tie to the limb depending on the type of bow you have
I, myself, am bias towards the limb driven. The forks on a limb driven stay up longer when you hit the trigger, thus stabilizing your arrow more. like a half way between a cable driven rest and a lizard tongue rest. However, if you are prone to jerk or not have the best form, it will magnify your lack of form (hit farther left/right/high/low, than you would with a cable driven). Keep in mind i am splitting hairs here, if we jerk, you probably wont hit the target with either rest.
I am also more apt to make the decision to things that are easier to repair, not that may be more robust. Things will break in my mind, the less time/tools/equipment needed to repair, the better.
The company you buy the rest from is a big thing as well. QAD, Vaprtrail, Hamskea Trophy Taker are all quality companies and I've dealt with all. Nothing against others but i have not dealt with them personally