The GTI will give you more hp from the factory, the TDI will give you better fuel economy. Both have a lot of potential. The TDI will be a low rpm torque monster with insane fuel economy while the GTI will have a higher rpm focus on horsepower and less fuel economy. It is a bit of a preference. Both would have a lot of power just massively different characters.
From the factory the GTI will be faster. After tuning it is less defined. Turbo diesels are very easy to get power out of. The difference in the end is that the TDI will get 40 mpg while making that power while the GTI will get about 25 mpg. :D As I said its a bit of a preference.
With the same ammount to each of work you may end up with power ratings like this..
It looks like a just a revo stage 1 remap on a stock Mark 6 Golf TDI will give you around 200hp and 290ft lb of torque. The stock GTI already has 200hp without a remap. With a remap it looks like 240hp is in range. The GTI may cost you the extra money just to buy the sport model. Both of the cars can benefit from exhausts, intakes, and upgraded turbos. With those you can get about 350hp from the GTI, the TDI with the same mods will only be pushing about 270hp but with about 430 ft lb of torque. Both are easilly modified cars. Either would be a great option.
This is pretty much correct except Revo is not a popular VW tuning company. APR is supposedly had the best tuning out there right now for the mkVI, for the GTi stage 3 would put you around 400hp and 400ft lb of tx. TDI is a little different... I haven't really seen any good turbo upgrade tunes for it. Not sure if the demand just isn't there or what is exactly going on with that. What I really dislike is the limited amount of options you have, its seems like more and more tunes that are put out are only for a specific turbo. I feel like with newer cars you are so limited on your overall options that your car loses personality and character. Might just be me but I am definitely more attached to my previous vehicles than I ever will be with my mkVI.