The answer to the question of whether modern Greece is unstable or not should be looked at in context. Greece, Spain and Portugal went through an interim stage of development after the dictatorship regimes they had fell. Greece was the first to shake off the junta in 1974 followed by Spain and Portugal.
Greece and Portugal are of similar size and have more or less same volumes in terms of economies and growth. The difference between the two is that whilst Greece had suffered from devastation as a result of WWII Portugal was not involved. One could therefore argue that given that Portugal did not face the destruction that Greece had to face due to the German invasion and occupation they should be doing better.
Spain was also affected by the civil war but there is no point comparing Greece with Spain as the second is a larger country with more resources. So a comparison with Portugal is more relevant.
We then had the rapid growth of the Greek economy. Greece became the 10th member of the EEC Britain having been the 9th. So they were not doing too bad.
Things went wrong with Portugal and Greece when Germany and France encouraged both countries to adopt the Euro. This was a disastrous mistake given the conditions needed to have a functioning currency. Portugal and Greece were wrongly thrown in the deep end because of the Euro project. Both countries will either have to learn to function with the prec conditions that are necessary or get out of the single currency. So the answer is that neither Greece or Portugal are unstable they were just not ready for fiscal union. If they want to stay in they must make supreme sacrifices and change the way they think and operate.