S3 Pros - 3 door looks, interior is nicer, red lit up vent dials, leather seats, better plastics, nicer place to sit. Quattro (well, haldex at least) big advantage if upgrading engine
S3 Cons - 3 door impractical, front end looks **** compared to an LCR, brakes are poorer,
LCR pros - front end looks loads better, brembo brakes, some have recaro seats, handling is supposedly better (have not driven S3 personally), cheaper to buy, MPG should be slightly better as lower transmission losses (although haldex system is supposed to be FWD up to loss of traction so not entirely sure about this one) 5 door practicality
LCR cons - back end is fugly, doesnt have the audi prestige, no option of leather interior as standard, traction can be an issue unless road is smooth and bone dry.
Both cars are pretty much the same and parts are pretty interchangeable - i.e. you can drop leather interior from S3 into an LCR... For this reason buying an LCR and upgrading interior to S3 level is cheaper than buying an S3 and trying to fit brembos...
I ummed and ah'ed a lot between the two before going back to another LCR. Had an A6 inbetween and gotta say Audi interiors are much nicer, but hard to justify the extra price tag. Main thing that swung getting another LCR was lack of 5dr option on an S3.
Hope this helps
Ben