PS: I have to wonder though how are you able to purchase those programs? Not wanting to sound mean, but I remember your earlier texts concerning Construct price and the 100usd Dev-lisense fee from Apple etc.
That was uncalled for... tsk tsk...
To the OP - I tried to get into Illustrator for the sake of the obvious scalability of the graphics... however I haven't had enough time to get into it enough. So I've used Photoshop mostly since I know how it works.
Just as the others said, whatever comes most natural to you is the tool that you use.
If you end up using Photoshop, keep it super simple (at least at first) and try to use Layers as much as possible. Separate elements so you can tinker on them individually. Makes it all a lot easier.
And also... Construct doesn't really display the PNGs as they show on Photoshop.. I'm not sure if the problem is on which end but some edges get drawn super weird so I've resulted to use the blending effect 'Stroke' a bit on the heavy side to counter the edge issue.