Dear seasoned travelers,
what is the cheaper option for 1 week?
Greece or Turkey?
If Greece, I'd visit Pylos, Mycenae, Athens, Delphi, Pella and Aristotle's school in Macedonia.
If Turkey, I'd visit Hattusas, Catal Hoyuk and maybe Durupinar (Mt. Ararat). Maybe even Karahan Tepe.

Thank you

I'm afraid I can't answer your question about costs, but I can say that I find it very difficult to imagine that you could see all the places you list in Greece in just one week.

You could probably visit Hattuşa and Çatalhöyük (both are amazing!) and one or possibly two other locations in Turkiye in one week. How much it would cost depends on what the additional locations would be, how you would travel, etc.

Best wishes for your planning!

GREECE
I suppose you plan to fly into Kalamata, rent a car there and drop it off at Thessaloniki, from where you will fly home.
Otherwise it would not be possible to do all that in 1 week.
But why just these places?
Most people who go to Pella and Naoussa visit Vergina too.
Similar remark for Tyrins and Nauplia which are less than 10 milles from the road leading from the Sterna exit on motorway 7 to Mycenae

TURKEY
You may check:
Day 1
Fliight via Istanbul into Igdir (arrival most probably in afternoon) plus bus to Dogubeyazit.
Sleep at Dogubeyazit and organize your trip
Day 2
Noah's Arch National Park
Day 3
Fly from Igdir to Ankara (only 1 plane daily, dp 14.15)
Days 4 and 5
2 days trip by bus and minibus to Sungurlu - Hattusas/Bogazkale and back to Ankara
Day 6
Early morning high speed train to Konya, local transport to Catalhöyük and back
Evening high speed train to Ankara
Day 7 fly home from Ankara