In addition to world type, a lot depends on what level you're playing at.
At Deity, for example, the AI has _huge_ production, science, and growth bonuses. This means that they expand even faster than a lot of people think is possible. In addition, only the first citizen in any town is content. This means that it is much more useful to rush-build with population than it is to try and build up larger cities that can compete with AI development. These two things lead to something like randomturn's vassal strategy or some other form of early military rush for dominance.
On lower levels the AI expands aggressively, but it is possible to keep up with it if you REX effectively. The larger cities allowed by happier citizens make it worth your while to avoid oppression unhappiness, and therefore it is often more useful to not rush-build too much in the early going. Without rush building it's a lot more difficult (though not impossible) to pull off an effective grunt rush in the very early going. Plus, the slower expansion of the AI means it might take longer before he builds cities close to you anyway. In the meantime, use REX for all it's worth!
It's my opinion that they two are not necessarily mutually exclusive, but my personal games are influenced by level. At harder levels, I _always_ use an early military expansion or else I get crushed. At Monarch and below, I start off REXing and then enter a later Ancient Age war if it seems beneficial.
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I'm not giving in to security, under pressure
I'm not missing out on the promise of adventure
I'm not giving up on implausible dreams
Experience to extremes" -RUSH 'The Enemy Within'
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