So I grabbed it during this rather nice sale and, completely unlike the first game which as far as I can tell uses the same engine, settings mechanisms, and etc, the second has severe problems with the right stick apparently. When I try to play, the camera just pulls left at all times and it's basically unplayable. If I switch the sticks, the character tries to constantly run left instead (plus I can't use the d-pad, so unplayable anyway.) The really funny thing is, the gamepad is well calibrated and as far as I can tell that right stick couldn't possibly be more dead center if I checked it with an ohmmeter... Anyway, out of desperation I tried copying the entire input folder of the configuration from the previous Giana Sisters game that gives me absolutely no troubles, and nothing changed -- it still pulls hard to the left despite the fact that the stick couldn't be better calibrated. As always, I can still play the previous game without this issue.

Actually that is a bug that existed in the original game as well. I'll try to remember what the solution was :)

Have you tried going into the options and remapping the input for the controller there (instead of copy pasting the relevant folder) ?
It sounds an awful lot like this old issue:
http://www.gog.com/forum/giana_sisters_series/camera_issues

My gamepad is a PS2 gamepad, so it has just as many buttons and analog sticks as a 360 controller. As for remapping, that was the first thing I tried doing. One of the biggest problems there is the configuration insists that it is receiving input during the calibration and thus will ignore it (and for some reason this means I'm not allowed to change anything related to whatever it thinks is out of calibration.) As you might guess, it's saying this about the right stick (even when I'm in digital mode and thus the stick is treated as staying full center at all times by the drivers.) Whether digital or analog modes though, the result is the same. The funny thing is, I can look in the control panel and I don't believe either stick is showing up as even a single pixel off center. Unless the dead zone is exactly 0.0 and it detects a 0.01 off-center as being movement (which would just be massively stupid) it is just outright wrong. Anyway, since it decides that the right stick is moving (despite the fact it is not) it will not allow me to remap the camera (but even if I could, like I said, this gamepad has exactly the same number of buttons as a 360 gamepad, so remapping means something else will be wrong instead even if I could do it.) Just to be sure, I even tried recalibrating it in the drivers just to be absolutely sure, but no change.

The previous game has absolutely no troubles with the exact same setup. Same PC, same gamepad, same videocard, same soundcard, same everything. The gamepad is even plugged into the same USB port. (In fact, I was playing the first game, getting annoyed at a level on it, saw this one on GoG and snatched it up to play for a bit to get my Giana Sisters fix, so I was actually coming straight from the first one to the second.)

That is extremly wierd. our best chance of getting help is trying the official forum. Then maybe the devs will take notice and have a solution (or will at least know to look into it).