This is a good way to frame the question. There is a lot of discussion about ideas of "Romanization" "creolization" etc, but it is very easy to forget the ways that the provincial experience was fundamentally contingent of specific historical factors. Thus, while, for example, both Gaul and North Africa experienced Roman imperial conquest, the circumstances around their conquest were very different, and thus from an individual's eye view, the outcomes were very different.

That being said, Greece did not come off very well in the conquest. Many places were ravaged by war, Corinth most notably, and this naturally had a destructive impact where it fell. But even areas like Athens, which was quite famously spared, were affected by the general catastrophe. Following this, in the first century BCE a series of wars took place in Greece that would have exacerbated this. More significantly, perhaps, is the political change. For centuries, Greek polities had been willing to aggressively use force to promote their mercantile interests. Rhodes, for example, used its navy to police the eastern Mediterranean. This was no longer possible after the Roman conquest, and the political backing for much economic activity was shattered. This is then related to the extractions of Roman tax farmers and administrators.

By the last first century, however, things had begun to look up. The military activities, and more significantly political settlements, of Pompey did a great deal to alleviate the problems with piracy in the region, allowing for more trade. The peace brought on by the end of the War of the Second Triumvirate meant that Greece was no longer being ravaged by armies fighting civil wars in her soil every few decades. And the political settlements of Augustus reformed provincial tax collection so that more of the profit from revenue gathering remained within the provincial boundaries. Greece never regained a truly central economic position in the Mediterranean, but the first two centuries CE were largely succesful for it.

This doesn't exactly answer your question, but you should read Celebreth's wonderful response to my somewhat similar question. In fact it won't answer your question at all, but it will help put you in the right framework to understand what's going on.