Welcome to the forums.
Put simply, Dark GDK is DarkBasic Pro for c++. They have all the same commands except you get to use c++ along with Dark GDK (so you can also use the windows SDK, etc.) while DarkBasic is its own language. I also believe that Dark GDK will run faster than DBP. I use DBP personally, and it is probably easier to learn if you don't already know c++. However, Dark GDK is free along with VC++ (express) but in order to sell your games, you must buy the Dark GDK license for $500 (I believe it's that). Depending on how much you want to learn, I would suggest DBP to start if it is your first language (you can always download the DBP trial and compare that to dark GDK).
With regards to the platform game, they have the same commands, so it doesn't really matter which one you use, but I think DBP is easier to grasp.