With regards to Crete both are great times and the weather will be lovely and hot too....however, the sea will be warmer mid September - but I really don't think that there is much difference whatever suits you better I would say :-)
Around the Cyclades, the water will probably be a little bit warmer in mid September than in mid June but generally colder than in Crete. The sea around Crete is much warmer. The exact temperature will also depend on the location of the beach. Both June and September temperatures (ranging from 23-26C) are swimmable.
You can compare average sea temperatures between June and September here: sailingissues.com/seawater-temperatures-gree…
Note that even on the same island there will be differences, with shallow bays warmer than beaches exposed to currents. Another factor to consider is the longer daylight hours of June.
In my experience the sea is quite a bit warmer in September than June in the Cyclades. Another factor to consider is that June is quieter than September. There will be more people about in September.
September, best time to go, weather still great, sea at its warmest, everything open, but fewer visitors than in July and August.
Hey early June is a lovely time in Mykonos. The sea is warming up and yet it is not crowded. You get good service in the restaurants and bars as well. Everyone is still fresh after the winter and I guess the place is cleaner.A big bonus I think is that the flowers are still out and the town streets are ablaze in colour and you get beautiful red and pink petals cascading everywhere. I'm sure you will enjoy it whenever you decide to go.
The one thing I dislike about early September is the number of cigarette butts mixed in with the sand. I don't find that to be a problem in June, but many high season beach goers seem to use the sand as an ashtray.
I've noticed that as well, Heimdall. I suspect I know why nationality is responsible. It's particularly noticeable on the part of Paranga beach with no sunbeds as there is non-one to clean them up. On some beaches, especially on Koufonissi, you will see people walking round with empty water bottles filling them with cigarette butts.
GreecemadUK, I admire your diplomacy! ;-) Steve_p53, that's exactly what happens. The south-facing beaches in the Cyclades got quite a scouring last week, and no doubt there will be several more winter storms to complete the cleanup.