No problem...but prepare yourself....I'm long winded.

First off, I've used the 5600, 5700 and now the 5800 group at length, thousands of miles on each group.

Brakes
-There was next to no difference between the 56 and 5700 brakes, neither were bad per se...but they weren't superb either. The 5800 is a completely different design, far better stopping power. I'm actually running the 6800 brakes because I wanted more "umph" and bought them well before the 5800 had hit the market.

*EDIT*...I'll say that I do not ride in the rain...so "wet braking" is a non issue for me. I do go to Kool Stop pads over stock by default.

Shifter
-I preferred the fit/finish of the 5700 over the 5600...they really improved lever throw and brake feel (they are also smaller). I'd say the "5800-vs-5700" debate is really 50/50...there's not a ton of difference between the two, they both are great.

Front shifting
-This is where the difference really start to show. The 5600 has very smooth lever throw, but the actual derailleur was only so-so. Where the action at your has was quick and decisive, the chain grab wasn't always the same. The 5700 took a GIANT step backwards here and by what I understand, it is primarily because they went to "under the bar tape" cable routing -vs- the 5600's external routing. The 5700 took considerable effort to shift Small-->big and I had to always hold the lever in spot for a second to make sure it grabbed. The 5800 fixed this and then some. Not only is the front shifting clean and crisp, the effort is FAR less than what it used to take...and the derailleur grabs so much faster, even suing my worn Praxis chainrings. This was a massive improvement.

Rear shifting
-Where the front was a huge improvement, the back isn't as large. When going from the 5600-->5700-->5800 the shifting has improved one step at a time. It is much easier to attain, and maintain that "sweet spot" rear shifting where the shift is not only quick, but almost dead silent too. With my 5700, I could never get it quite right...always dragging just a touch in shifts, I even tried a 5700 and 6700 cassette...it made no difference. The 5800 is a decisive "click" darn near 80% of the time. The 5800 also adds more derailleur positions do help eliminate cross chain rub.

gearing
-I cannot say this is a "5800 is better than 5700" thing...but so far, given my current setup, the 5800 has been much better. An 11-28 in a 5700/5800 is as follows:


11-12-13-14-15-17-19-21-24-28 (5700)
11-12-13-14-15-17-19-21-23-25-28 (5800)

Using a 52/36 up front...I spend a vast majority of my time right in the middle of the rear gear...but...there a times when I had to do a transition from large-->small because I do not want to cross chain the 52. If you look at the difference in the 5700-vs-5800 cassette, the only difference is in the gears after 19. The 5700 has a 21-24-28 where the 5800 has 21-23-25-28. Those changes have allowed me to stay in the 52 more than I used to when the going gets tough...but not tough enough to switch to 36.


So...in the end, the 5800 package is just a much nicer overall set than the 5700. I've been very pleased with it.