There aren't any significant differences between the two 'boxes, at least in the aspects that you write about so you shouldn't expect any big surprises. Yes there's a slight lag of pulling away, had this in all 3 different DSG boxes I've driven but you learn to anticipate it and S (at least stock) is practically useless, even more around town as it needlessly holds each gear for too long.
After 8 years of DSG driving, I only drive in D when I'm commuting during rush hour and know there is no point in trying to enjoy the car. Any other occasion or time of day i stick it in manual, mostly using the paddles but occasionally the stick as well for old times sake and enjoy.
Being your first semi auto it will feel a little weird at first but give it time and don't be afraid to learn Manual mode and you will most probably love it. Forget that: You do have to drive the car in manual mode also, otherwise you are not experiencing what it has to offer to you if left in auto all the time. The beauty of the DSG and what most manual transmission fanatics ignore is the control it gives you over the car and how to use the engine's torque to your preference the exact same way you would do in a manual car (you could even keep the old habbit of resting your right hand on the gear level all the time - i know some people do). It's not hard or complicated and you can't break anything or do something very wrong as the 'box will protect itself from mis-shifts. Just push the lever to the left and off you go. Now you decide about everything just like in a manual car. Want to hold on to a gear for that bit longer in order to help acceleration? Sure, the car will let you do that up to the rev limiter if you like. Upshift early as you want to settle to a fixed speed and low rpm asap? Just flick the right paddle or push the stick forward briefly. Use the engine to brake? No problem. In fact the only thing that's different between a DSG's manual operation with the stick vs a MT is that you don't move the stick around in an H pattern but rather forward and backward but that's hardly what creates the so called "involvement" with the car is it? It's about controlling and using the engine's output to your exact preference and you can perfectly keep doing that with a DSG.
The pedal box is not related to the gearbox, it's the way VW maps the throttle on its cars, even performance models. It's a very significant improvement, especially once you try it on, but I'd say learn your car first, especially the DSG being new to you and you can at any point decide to go for it.