Regardless, the YC application is pretty much perfect for this type of program, so I can understand that they didn't want to mess with something that worked. Plagiarism is a high form of flattery. The three or four changed or new questions make the TS application worse than the YC one, they shouldn't have bothered.
A venture capitalist is one of the founders of TS -- PG sees that as a negative but it could make it easier to get money from a friendly venture capitalist or provide insight into the notoriously obtuse mind of a VC.
TS also has more than one session a week. I see that additional structure as a good thing but I'm sure PG would argue that it's taking time away from hacking.
The website of each company certainly shows a difference in mentality -- YC is stylized minimalism, TS is over the top web design you get when you pay someone too much to design you a site.
So what should you do? Apply to both. Don't sell yourself short. Boulder's a nice city. So is Boston (even though the trains don't run past midnight).