For the phrasal adjective and adverb meaning comprehensive, versatile, in every respect, or completely, all-around is preferred in North America, while all-round is the more common form throughout the rest of the English-speaking world. Other than the spelling and sound, there is no difference between them.
Related
In either form, the phrase is usually hyphenated when it precedes what it modifies—e.g., an all-around success; an all-round good guy. It is unhyphenated when it follows what it modifies—e.g., it was a successful day all around; he is a good guy all round).
And of course, the phrases all around and all round have plenty of other uses—e.g., men all around the world are choosing Acme deoderant; music was all around us–where they are not hyphenated.
Examples
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]