Dizzee Rascal, Liquid Room, Edinburgh

It's surely going to be a new sensation for Dylan Mills, also known as grime figurehead Dizzee Rascal, to embark on this national tour and not hear the biggest cheer of the night the moment his previously defining track "Fix Up, Look Sharp" is played.

Five years have passed since Mills's debut album Boy In Da Corner won him the Mercury Prize and, in all honesty, it's taken the same five years for him finally to make the jump from critical cause célèbre to mainstream recording artist. The fact that "Dance Wiv Me" – the song that saw Mills and dance producer Calvin Harris jointly occupy the UK chart's No 1 position for a month this summer – is a blend of grime, nu-soul and electro-disco might have offended the purists, though.

It's hard to decipher at the moment whether Dizzee works best as an austere and rough-edged musical ambassador for the meaner streets of London or as the kind of universal success story whose retirement plan might involve greatest hits tours of provincial nightclubs. Yet a blue-sky outlook might have hoped he could have found his way to universal acclaim without sacrificing so much of the style he helped to create and develop.

Still, it's not as if Mills looks bothered by the fact that "Dance Wiv Me" seems to have reinvigorated his level of national recognition. This show was sold out and would have been so in a much larger venue, which is impressive considering that grime is more of an enclave interest than an overground one in Scotland.

Arguably, though, it's Mills's accent and background that identify him as a grime artist more and more these days, because his musical style and onstage persona are crossing over into the realms of straight hip-hop. The Dizzee Rascal lexicon has morphed into a more worldly, transatlantic style than the East London pirate radio chatter of before, as is in evidence when he informs that "right about now we find out where the Gs are".

The G is for gangster rap over grime, and it's a sentiment that has more in common with the bling-bedecked worlds of huge US stars like Jay-Z, Puff Daddy, 50 Cent et al. The track which follows, named "Where's Da Gs", does start with the anachronistic diss "liar, liar, pants on fire", but it's otherwise your typical throw-down to an unnamed rival who ain't all that.

"So this is Edinburgh," says Mills after the track has finished. "Capital city – top dogs of Scotland, yeah?" There's been an air of territorialism about the Dizzee Rascal show since last year's Maths + English album; he was never so forthright in his previous work. The new model Dizzee is just as likely to warn that you'd "better run when you hear the sirens coming" as he is to make some kind of more muted social comment.

Boy In Da Corner's "Jezebel", for example, is one of the set's more thoughtful highlights. Mills still throws up plenty of visceral imagery in his near-knuckle lyrics, but the tale of a promiscuous young girl who ends up pregnant is affectingly told, beneath it all: "Two fatherless kids / One single mum / No longer young / But the boys still come". The same album's "I Luv U", again about teen pregnancies, is also powerfully bleak, and it would be a shame if this relative sensitivity in Mills's work were to be submerged.

Yet here we are with Dizzee Rascal and his MC, stripped to the waist and baggy trousers hanging down about their thighs in gangster style, singing "Excuse Me Please" and cocking their middle fingers in the air come the line "there must be hope... for revolution". He is, of course, still a wildly engaging and entertaining performer, but it seems a shame that he has to play the same game as his US counterparts to have any access to the huge rewards they've enjoyed.