I suspect that startups are for more creative people. So you need to decide whether to pursue an analytical phd or a more creative startup. BTW, you might find this discussion interesting: http://weblog.fortnow.com/2006/07/science-and-art-of-computation.html
As someone who did a PhD in a creative kind of computer science field and felt frustrated by the success of those who choose more trodden PhD paths - I was going to agree with this. But in start-ups as well as PhDs success is defined by the number of people you give value to not how creative you were.
There are different forms of creativity, some more open-ended than others. Most research done in scientific fields is not what I would call open-ended creativity. BTW, the most creative idea I have seen recently actually came from the Univ of Washington & Microsoft Research: http://labs.live.com/photosynth/. The most creative one prior to that came from a phd student @ CMU: http://video.google.com/videoplay?docid=-8246463980976635143. It would be interesting to see what percentage of successful startups are conceptually clever with mind-blowing ideas such as these. As an example of one, I really like http://www.likebetter.com/.
