It's somewhat lost with the removal of the lyrics, but the entire theme of the JP music is to have confidence and believe in yourself. Sonic's got the skills, what's he have to worry about? Besides the US music making him more depressed and angsty than Shadow, that is.
Wha? Sonic Boom is about confidence, too. If you're strong, you can fly, you can reach the other side of the rainbow. It's alright, take a chance, cuz there is no circumstance you can't handle when you use your mind.
Toot toot Sonic Warrior starts out with...
Excalibur -- It's not that far
What do ya make? -- Give and take
Goin' home -- Time zone
Check out Egg -- He's never alone
Leather and lace -- Kickin' his booty
What do you get? -- Say, fast jet
Doom room -- Cosmic zoom
Heads up, Jake -- It's Sonic Boom!
...um... wat?
Sonic Boom just takes the message from the rest of the song and turns it into something that actually sounds good.