nickxyzt wrote:
Could anybody point out what is the difference with the next diagram? What am doing wrong?
2 is not 100% sente, black can choose to play 3 elsewhere depending how big other moves are.
The reason the hanging connection is (usually) better than solid is if white tenukis, then you can increase your territory and eyespace in sente (notice how
means white can't capture 
if black now tenukis):If you just played solid, then you'd need to end in gote if you want to defend
The reason white should play atari as in your second diagram is it makes black's 2nd line move there gote instead of sente.
A more subtle advantage of the hanging connection over the solid is that it makes better eyeshape: Imagine white plays e3 as a ko threat and black ignores (or through some other fighting in this area black gets cut off here), he can live unconditionally in the corner:
With the solid, it is only a ko for life in the corner (tripod group with extra leg):
There is a possible advantage of the solid connection though, that is if you don't expect the additional eyeshape of the hanging connection to be useful and in the yose you wish to play this sente yose sequence. White can try to prevent black making this sente profit by exchanging b3 for b2 (if black ignores then white's block at b2 is big and sente to capture 3 stones) so that it reverts to the hanging connection shape with just the gote capture as black's yose here. Which of these outcomes is more likely basically comes down to who will have sente to start the endgame, which is not an easy thing to say.
, the result is no different then if black had pushed at 
, white blocked, black descended to