"Better" is an unsuitable category, but "richer" definitely applies. The East did not "have Egyptians" but they did have the economic surplus of Egypt, the most fertile (and likely also most highly taxed) province of the entire Empire.

What you need to weigh against one another is the number of legions needed to control or pacify a region on one side, and the relative economic vitality of a region on the other. In that respect, a province like Dacia was a sinkhole for the Empire's funds, while Sicily, Africa, or Egypt were assets. As somewhat of a chimera in this respect, Roman Syria was both very rich but also swallowed up tremendous resources due to its large contingent of troops.

As a rule of thumb, the East probably had more financially potent provinces, with Egypt as the pivotal one being almost entirely state-run if you will (the Emperors had inherited the Ptolemean royal taxes fairly directly, and apparently kept their control over these assets until the Muslim conquest, aside from a few rebellions).

The only comparable money-maker for the West was Africa, which in the course of the period of migrations de facto seceded from the Empire, and after 430 fell to the Vandals. The West was also plagued by the fact that many of its provinces were less urbanised and more agrarian than the East (especially after the civil wars of the 3rd c. AD), and that the original urban elites of the civitates (the provincial upper crust, aka decuriones) were either becoming too powerful to be effectively taxed by the susceptores (tax officials) or too economically marginalised to contribute at a useful level. At the same time, the political and economic elite of the West, the Senatorial class, apparently succeeded in securing and increasing their own wealth. They seem to have contributed less and less towards public expenses, retreated from the urban centres towards their rural latifundia, and through a system of protection for labour seem to have alienated a large number of landholders from the fiscus. In other words, they laid the foundation of what we later on recognise as proto-feudal landholdings, on which a lord of the manor is the only direct authority over a tenant farmer, who exchanges his labour for protection. We have indications that the richest of these senators ended up with a higher yearly income than the fiscus of the Western Emperor himself!

This is only the economic side of things. The military / ethnic side is another matter, but in my view all it did was exacerbate and trigger an already untenable economic imbalance. Eventually, the tax demands that the Western Emperors made on those subjects that remained within their reach seem to have contributed to an indifference or outright hostility on the part of their subjects when it came to resisting the barbarian "invaders" who began to usurp imperial power within the Western Empire (Goths, Burgundians, Franks, mostly).