I currently have the HTC One x and love it more every day. When it comes to power, they may be a little over your budget but there are a lot of opinions about these phones.
The Galaxy nexus is a great phone but there are a lot of complaints when it comes to battery life, some people even carry two batteries all day. It is a strong pone, but suffers in battery life. Its stock android feel is pleasing, but some people like a company's overlay better (Love Sense 4.0) It is the first phone to officially have Jelly Bean, but it is not the last, the one X even has an amazing port.
The One X will always be my first choice. I have it and love it. Although there are some phones with slightly better specs, the performance speaks for itself. I have noticed some slight lag because sense slows the phone a little, but 4.0.4 seems to have fixed most of it. Its 4.7" screen is even better than the iPhone's screen in my opinion. The screen is just beautiful and is one of my favorite parts of the phone. It is so close to its strong gorilla glass that it looks panted on! It has one gig of RAM but I must say that it uses it well.
The Samsung Galaxy SIII is another powerful phone that has been seemingly in competition and comparisons with the HTC One X and they always seem to come down to bias opinions and preference. I personally do not like the phone very much. in my opinion, I feel that the One X had a lot more thought in its design. I feel like Samsung was trying to do as much as they could to go against the accusations that Apple has when it comes to their design. If you look, the design is the complete opposite of all the accusations. The screen is not very bright in comparison to many other phones, despite being an AMOLED screen. The UI is just personally not my favorite. I feel it is fluid but still has some hints of gingerbread despite being on 4.0. it has about 2 gigs of RAM, that isn't badly used.
The HTC Titan II is a great Windows Phone, although I do not suggest getting it. The Windows Phone UI is really brilliant and I would love to have the phone but the One X won me over. I do not suggest getting it because it will not be getting the Windows Phone 8 Update. If you want a Windows Phone, I suggest that you wait for a new release (Hopefully a Titan III!) It has support for higher screen resolution and NFC. I think Windows Phone has a lot of potential.