Both months offer a genuine shoulder-season experience, but they suit slightly different travellers. June arrives earlier in the season: the sea is around 20–22°C, daylight hours are longest (the summer solstice falls in late June), and most beach bars along the coast have just opened for the season with full menus and fresh energy.
September has the advantage of a warmer sea — still around 23–24°C in early September — and the golden late-summer light many photographers love. Crowds thin noticeably after the first week of September as European school holidays end. The downside is that some facilities start scaling back toward the end of the month.
A practical tip: if your priority is beach-bar nightlife and full service at every venue, late June through early July gives you the best of both worlds — tolerable crowds and everything open. For pure relaxation and warm water, the first two weeks of September are hard to beat.