For the TSU7000? Although I'm a big Corel fan, I'd have to say Photoshop for bitmap editing, simply because I discovered some absolutely HUGE (and from further testing long-standing) PNG transparancy bugs in Corel Photo-Paint. In fact I have a huge list of "final result quality issues" that can be found in Photo-Paint (I was an official Corel beta tester for 4 versions, but ever since Corel 12 they've cut back and done all testing only in-house... and it shows.) Photo-Paint's easier to use, but Photoshop's output is better.

However, I still much prefer CorelDRAW over Adobe Illustrator for vector editing, but if you really do want to start your designs in vector format it's likely going to have to be a personal choice there.