<p>What are the main differences when using ABS over PLA and vice versa?</p>

Paraphrasing
this
site. Feel free to add suggestions in the form of comments and I will try to incorporate them.
Summary
ABS: Stronger, machinable, more flexible, and more temperature
resistant than PLA. Typically printed on a heated bed. Warping is a common problem when printing ABS.
PLA: Wider range of filaments available, easier and in some cases faster to print. Not as strong as ABS and the fact that its biodegradable could be seen as both a benefit and a drawback.
Material Properties:
ABS: Strong plastic with mild flexibility. Naturally beige in color. Can be filled and sanded. Higher temperature. Easy to recycle.
PLA: Not as strong as ABS but more rigid. Naturally transparent. More difficult to fill and sand. Can sag in hot temperatures. Sourced from organic matter so it can be broken down in commercial compost facilities.
Part Accuracy:
ABS: Part warping is a significant issue. Sharp corners will often be rounded.
PLA: Less heat required contributes to less warping. Becomes more liquid at common extruder temperatures so finer details can be printed.
Safety and Handling:
ABS: Strong burning/melting plastic smell is present when printing ABS. Health concerns have been raised regarding airborne ultrafine particles generated while printing with ABS (
ref
). ABS will absorb moisture causing popping when the moisture enters the hot end. This leads to discontinuities in the print job.
PLA: Doesn't smell as strongly when printing due to its organic nature. Moisture can also be absorbed into PLA and can irreversibly damage it.