I am planning a trip for a week or so in June. I would like to visit either Prague or Greece and I was curious as to what those on this forum suggested. Thank you!

I'm sure you didn't intend for your question to sound this way, but it comes out as a request to compare a country to a city. Hard to do, even if we try to take the best assumption. Pick a city in Greece, or ask for a choice between 2 countries.

Let's assume you try to choose between Athens and Prague. There's ancient history and clutter in the one, and more recent history and beauty in the other. Which would you choose?

You cannot go wrong either in Prague or in Greece (as a whole) but Greece would bring a far greater variety of individual sites, obviously. If you are "into" Medieval then Prague would be the place; anciet sites and ruins, then Greece. June is still a good time for Greece when the heat isn't quite as high and the sun so intensely blinding. I would suggest going to the "classic" sites to include Corinth, Delphi, Olympia, Epidaurus and try to tet to at least one or two of the islands such as Santorini or Mykonos.(Crete's fine but I think it just continues the "ruins" theme.
Athens?? great for a couple of days and then leave the exhaust fumes, etc., behind.
Prague...gold leaf for days in churches, on buildings; magnificent castle and like stepping back into time.

Hard decision; wish you could someday do both as I have and never regretted either. Enjoy your journey.

I can't make a comparison since I have never been to Prague but, since Greece (Athens and islands of Santorini and Folegandros) was one of my least favourite places, I would go anywhere else.