(I have read much more extensively about Phoenician expansion into the western Mediterranean, so someone else would probably have more insight into the internal Greek dynamics which led them to colonize outside of Hellas.)

But to quote Maria Eugenia Aubet from her book The Phoenicians and the West: Politics, Colonies and Trade: "The Greek enterprise seems to have derived from colonialist ideas, and the Phoenician enterprise to have been content with founding trading establishments close to indigenous communities." In short, they had different motivations for setting up colonies, and thus experienced different outcomes. And while their are some obvious similarities in the earliest colonial expansions by both civilizations - establishing trading posts to find raw materials - their colonies developed in far different ways.

The Phoenician expansion, led by Tyre, has to be seen through the lens of their delicate role as intermediaries between Great Powers (chiefly Assyria, also but Egypt and Persia), their relationships with neighbors like Israel, and role in the burgeoning economies of the western Mediterranean societies (Tyre's trading partners in Spain, Portugal, Italy and N. Africa). Tyre, a mercantile power, had a long-term strategy to make themselves, or more specifically, their kings, priests and councils, irreplaceable: they had a powerful a monopoly supplying raw metal ore to Assyria (and Egypt, Persia, and the Canaanite states), and in the production of certain manufactured goods. In exchange, the Punic city-states received hundreds of years of peace and preferential treatment by the Assyrians (Assyria at one point forcing one of Tyre's upstart vassals in Cyprus into resuming paying tribute) and a reliable flow of agricultural foodstuffs (Israel had plenty of grain to trade, and no one could supply its kings with fine pottery, linens, lumber and ore quite like Tyrians).

The lure of metal - silver and gold for coinage, copper, tin and iron for tools - is paramount. The earliest Phoenician colonies, Kytion and Carthage (Carthage is the Latinization of Punic Qart Hadasht, or "New City, City referring in both Cypriot and African Carthage to their mother city Tyre) in Cyprus and Gadiz in Andalusia, were established to monopolize metal sources. The Phoenicians not only trades raw metals, but operated factories and refineries to shape those metals- the western Mediterranean had it's own indigenous economy, fueled by Phoenician ships and advanced Phoenician smelting/metalworking; carbon-dating reveals a plethora of Greek and Italian goods found their way to Andalusia far before those societies themselves began to expand. These metal-centric settlements were also the first to expand, doing so out of the resource surpluses. Gadiz, modern day Cadiz, was the trading partner and refining center for the Iron-Age Kingdom of Tartessos in southern Spain, which was itself founded on the Rio Tinto mining complex; after the Phoenicians introduced their more advanced metallurgical techniques, the complex' production exploded, and the quantities of gold, silver, copper and iron overwhelmed the Tyre-Gadiz trade route, allowing Gadiz itself to create new satellites to trade its excess metal for both different metals and agricultural goods. All these colonies, you may note, are dependent on shipping routes for survival - the vast Phoenician trade hub was it's own unique organism.

Metal was a powerful magnet magnet for the Greeks as well, but moreso than Tyre and its sisters, the Greeks also founded agricultural colonies to immediately relieve mainland overpopulation and create new sources of food. Tyre also dealt with overpopulation and food crises - it was the premier Mediterranean city, with its metropolitan area stuck on a small island, and it's hinterland constrained to suburbs and farmland not much larger - but for whatever reasons, found the solution in Asia instead of its Mediterranean colonies: Tyre expended a great deal of energy and resources founding settlements near the Tigris, intimidating its Canaanite neighbors and in turns negotiating/warring with Israel for both agricultural products and access to its hinterlands for settlement. Greece, without agriculturally productive neighbors of its own to trade or war with, instead relieved their demand for food with a sea-borne colonial enterprise. It is unclear just how united or disunited the cities of the Canaanite coast really were on the whole; it seems that Tyre's hegemony came at the expense of Byblos and Sidon, and that Tyre did little to protect its siblings from predatory states.

I mention this disunity because the simple fact that Tyre alone was the chief Punic colonizing power means simply that there were fewer colonists (Carthage's dominance only came about after the sacking of Tyre by Alexander the Great around 330BCE, when a flood of refugees brought their wealth and manufacturing expertise to the city), and because the lack of a united identity contrasts with the emergence of Greek identity, culture and the conception of the polis.

The Greeks incorporated their overseas colonies into their conception of Greater Hellas, and those trading centers lucky enough to both tap into trade routes and overlook fertile land became polis' of their own - city-states whose Greek-speaking citizens were awarded recognition and rights. And while many Greek mother-cities were exploitive towards their colonies, they were nowhere near so much as Tyre, Sidon and Byblos. For the Phoenician city-states, colonies existed only as an aspect of of the trading network, vital as they may have been. Those differing conceptions of the colonies would, however, conversely affect their relationships with the indigenous populations.

While Carthage would later develop aggressive land-grabbing policies in Africa and Spain, the initial Phoenician traders had almost universally peaceful interactions with their neighbors. To risk disrupting trade would risk upsetting the delicate balance of their political organism. The presence of Greeks, however, accompanied the eradication of nearby natives in mainland Italy, Sardinia and Sicily (then called Magna Graeca due to its large Greek population and powerful city-states); the polis had a both ideological and strategic interest in self-sufficiency, even if it came at the expense of the previous tenants of their farmland. While Greeks did also transmit their culture through peaceful means (Marseille was peacefully settled, and their Celtic neighbors in southern France were ravenous for Greek cultural products), they, unlike the Phoenicians, appear to have had a stronger appetite for ethnic conflict stemming from their binary conception of the world and its moral order: Greek v. Non-Greek, and unlike the Phoenicians, carried their martial traditions to their colonies.

In the late second half of the 1st millennium BCE, Tyre's exposure to violence and conquest at the hands of Assyria, Babylon, Persia and Macedonia would wreak havoc on its mercantile empire; Greece was spared conquest by all these save for Alexander, who, fortunately for them, was also ideologically invested in preserving Greek culture at home and evangelizing it abroad. A disastrous war in Sicily would result in the expulsion of Phoenicians from the Hellenistic sphere, and the infamous Punic Wars would remove the inheritor to their empire, the Carthaginians, from Spain and Africa and utterly erase the most powerful Phoenician city-state since Tyre.