Versatile, many-sided, all-around can all mean marked by or showing skill or ability or capacity or usefulness of many different kinds.
When applied to persons, versatile stresses aptitude and facility in many different activities requiring skill or ability, especially the ability to turn with no diminution in skill from one activity to another without a hitch; applied to things, it stresses their multiple and diverse qualities, uses, or possibilities.
Many-sided applied to persons stresses breadth or diversity of interests or accomplishments; applied to things, their diversity of aspects, attributes, or uses.
All-around implies completeness or symmetry in development, either general or within a single activity with many phases; the term need not imply special or great attainments but rather a general ability to do oneself credit; when applied to things, it implies an analogous general usefulness.