For what it's worth, I own both a 2011 Audi A3 6MT with S-Line package (same chassis and engine as the Mk6 GTI) and a 2004 Honda S2000 AP2. I've also test driven 2 different FR-S, one with the TRD body kit, wheels, exhaust, etc, and one stock.
As for the Audi, it's my daily driver and I find that it fits my needs almost perfectly for its intended purpose. It's fairly comfortable and spacious with quick acceleration (with a tune and intake it should be pushing 240-250 bhp, 290-300 ft*lb) and a very usable torque band. The turbo spools quickly from 2000rpm and I don't need to downshift nearly as often as I do in the S2000. Compared to the FR-S, it's just so much quicker and more practical for every day driving. The interior is also really nice with leather/alcantara seats and soft-touch plastics. I hate the plaid seats in the GTI. They are just so ugly.
Pros-
1) Fairly quick from the factory.
2) Has tons of engine tuning potential. A simple $600 Stage 1 ECU tune takes the engine performance to another level.
3) Looks great in and out.
4) Fuel efficient. 21 city, 30 hwy. I've gotten up to 36 from just freeway driving at 65-70mph.
Cons-
1) German and expensive to fix once warranty's out.
2) FWD means torque steer (after the tune) and TONS of wheelspin when WOT in 1st.
3) Ride could be a bit more comfortable, though I do have the S-Line sport suspension.
4) Barely any engine noise inside the cabin, and I'm someone who likes to HEAR the car when driving hard.
5) Brake pedal is spongy, gas pedal is floor-mounted so it's harder for me to heel-toe.
Now for the S2000 AP2. I completely agree that it's a pure sports car, even in comparison to the FR-S/BRZ. It feels way more raw and less forgiving, and really pushes you to become a better driver. It can be scary taking the car to its grip limits. It also makes an awful daily driver with all the cabin noise, harsh ride (mine is on Bilstein coilovers), and powerless engine below 5k rpm. But hey, that's not the point of the car, is it? As a 2nd car it's everything I want it to be.
Pros-
1) Sublime handling and good acceleration when revved.
2) Looks absolutely sexy in every way, especially with red/black leather seats.
3) You can feel the wind in your hair and the sun on your shoulders on a nice day.
4) Typical Honda reliability.
Cons-
1) Uncomfortable as hell. I'm only 5'7" 160lb but the seats still make me feel like I have arthritis after an hour. Part of this may be due to the coilovers, but I doubt the stock car is much better.
2) Lots of cabin noise even with the top up.
3) Soft top rips easily and can be broken into.
4) Terrible fuel economy. I average under 20mpg.
5) Somewhat pricey for an "old" car due to demand and semi-rarity.
Where does the FR-S/BRZ fit in this picture? It's a compromise. It's comfortable, usable, efficient, semi-spacious, and still a sporty drive. I still contend that it's a true sports car, even though it's not that fast and has a so-called back seat. All the driver inputs are characteristic of a sports car. Steering, pedals, shifter, and seating position are all pretty much spot on. I did, however, notice the braking issue the OP mentioned. I definitely had to press the brake pedal way down just to get any stopping power. Not sure if this was just the car I was driving or if it's a common issue.
Photos of my cars:
(The FR-S is my buddy's)