I can't answer your question about Roman colonization, but I'm afraid the assumption on which your question is based is wrong. Greek settlement throughout the Mediterranean probably wasn't due to overpopulation. In fact, most of our evidence suggests that population levels had nothing to do with it.

Admittedly, it's clear that the population of mainland Greece was growing in the 8th century BC, which is the time of the first major wave of overseas settlement. There are more and larger inhabited sites throughout Greece than ever before, and those sites also leave more burials with more objects in them. Some of this growth is clearly resettlement rather than expansion, and the increase in burials must be explained in part due to changing burial practices rather than a larger number of people dying, but even so, there's an overall picture of some gradual population growth.

It is very difficult, though, to tie such growth directly to settlement overseas. For one thing, survey archaeology shows that there was plenty of unused land in mainland Greece that could have been used for agriculture, but wasn't actually brought into cultivation until the 6th century. For another, there is no indication that the Greeks ever gave up the practice of keeping vast numbers of slaves, even though these would have put enormous pressure on a subsistence economy supposedly unable to feed even its free population. For another, the distribution of "mother cities" said to have sent out settlers in the Archaic period is very uneven. A few communities (Corinth, Eretria and Chalkis, Miletos) are linked to the settlement of dozens of new cities, while other major centres (especially Argos) never founded a single one. Are we to believe that only a few parts of the Greek world enjoyed explosive population growth, while others were not affected? Archaeological finds don't support this.

When we look at the reasons the Greeks actually offered for overseas settlement, overpopulation is not among them. Land hunger was a factor, it is true - but shortage of land could be caused by any number of factors, including accumulation of property by the elite (an endemic problem in Archaic Greece), desire for status through land ownership among people who could also make a living by other means, and natural disasters such as droughts or flooding. We should probably see land hunger as closely tied to another motive often suggested for Greek overseas settlement, namely the search for resources and markets for trade. All of these were ways to increase one's weath and social standing. As long as resources and land were available, there would be Greeks willing to sail long distances to acquire them.

This economic opportunism ties in with the information we get about particular founding efforts, like the Parian settlement of Thasos or the Theran foundation of Cyrene. In each case, only a small core of settlers was actually sent out by the city-state that took the initiative. The rest of the new settlement's population came from all over Greece - a motley collection of outcasts and fortune-seekers, referred to be Archilochos as "the misery of all the Greeks". Often the initial group consisted of a disaffected political faction or a distinct group within the home community, looking for a new place to establish itself independently.

All this is quite different from the story of Classical Greek colonisation, which much more often had a clear geopolitical motive. Initiatives like the Spartan settlement of Herakleia in Trachis or the Athenian settlement at Breia were attempts to establish a loyal bastion from which power could be projected regionally. Again, these initiatives had nothing to do with overpopulation. However, at least they represent the sort of conscious, deliberate government effort that your question presupposes, and that probably also characteristed Roman colonisation - but not so much the overseas settlement of the Archaic Greeks.