I would recommend Audacity for re-encoding.
http://audacity.sourceforge.net/(If you are on a Mac, hit the 'download' tab and there are Mac versions for it too! I'm guessing you're not on Linux, using your iPhone...

)
Tom encodes his oggs with a pretty high quality, so the degradation you get for re-encoding into mp3 should be minimal as long as you also use a high quality on the mp3 encoding.
As for whether Ogg is better than mp3... I'm not going to debate that but I'll point out that Betamax was believed to be better, and it didn't become the defacto format. Many compression formats came out to compete with Phil Katz' ZIP compression, many superior (ARJ's spanning abilities were much better), but ZIP still became the standard. Sometimes... what matters most is not whether something is better, but whether it is the most widely adopted.