Além da soletração e do som, não há diferença entre as expreções.
Around vs. round
Em ambas as formas, a frase é geralmente hifenizada quando precede o que ela modifica.
Ex.: an all-around success; an all-round good guy.
O termo não é hifenizado quando segue o que ele modifica.
Ex.: it was a successful day all around; he is a good guy all round).
E, claro, as frases com all around e all round possuem vários outros usos, como por exemplo: men all around the world are choosing Acme deoderant; music was all around us– onde não são hifenizadas.
Exemplos
Hernández, who has played in 33 test matches for Argentina, has great all-around skills. [New York Times]
But despite the well-trodden ground, it finds its own patch thanks to an up-to-date landscape of economic hardship and all-round criminal incompetence. [Guardian]
He was described as an all-around nice guy. [CBC.ca]
The regional grand solution is going to require compromises all round. [New Zealand Herald]
On an afternoon that contained much frustration all around, the Denver East senior defensive back picked off a pass and returned it for a touchdown. [Denver Post]
Andy is an all-round footballer, but because he is 6ft 3in and one of his strengths is his aerial power, everybody dismisses the ability he possesses on the floor. [Irish Times]
Pennsylvania dance instructor and all-round ogre Abby Lee Miller has a rather unkind way of ranking her troupe of tiny dancers after each performance. [The Age]