Standard front is a twin-piston aluminium AP calipher. Rear uses a sliding calipher (single piston) from Brembo.
All brake discs on the car are identical (no difference front/rear). Actually there even *is* only one brake disc type used on the S2. No difference in left-right either.
When using race brake pads (Eg. Pagid RS14) you get very good brake results. Stopping on a dime so to speak. Factory pads are OK, but not that great on the track.
Don't go overboard though.. Pagid RS15's are even more 'grippy', but these are too much for the Elise and you lock up too quickly. Not enough control/feel about the braking.
Brake 'upgrades' are usually done to reduce weight as the rear calipher is a cast-iron lump and weighs a lot.
As such Lotus-Motorsport moves the front caliphers to the rear and fits new aluminium 4-pot front caliphers.
This is not road-legal in europe though as you lose the handbrake function of the rear brakes (integrated in the standard rear brake caliphers) and that's a requirement..
Another upgrade is usually aftermarket brake discs using an aluminium center 'bell', so the brake disc material becomes replacable separately. (OEM lotus brake discs are often said to be 'made from toffee' and tend to wear fast.. Aftermarket often get better results for a lower price..)
Bigger brake discs are not used very often. The car doesn't really need those unless you are a *really* good driver, have oodles of HP and like to brake at the 50ft mark before a corner.. (and they weigh more too!)
There are some issues with the brake balance between front/rear, but most people seem to cope OK by experimenting with different pad compounds front/rear.
There is a big brake kit coming out now from racespeed, but don't think anyone sees the point particularly as you can lockup the wheels just fine with the current setup. I guess if you are getting fade on the track it might help, but given that the upgrade is only coming out after so many years, it indicates that its not thought a serious problem.