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People are only looking at the price side of things, but there are other factors that weigh pretty heavily. These combined units (fan + AC) usually have a weak internal air conditioning unit - like those models they sell in department stores. You end up paying more because of the integration, but you get an AC that cools like a souped-up fan, nothing special. If you live in a small space and really just want ventilation with super light cooling for less hot days, maybe it's worth considering, but for actual hot weather it won't cut it.
The real problem is when one of the two fails, you're out the whole thing. Imagine the fan motor burns out - you're left without AC and without ventilation at once, and the repair gets expensive because it's a specific and less common part. With two separate units you have redundancy: one breaks, you keep using the other while you get it fixed. Plus, in terms of control, do you really want ventilation without AC? With separate equipment you can do that, with integrated you don't have that flexibility.
My vote is: keep them separate. It works out cheaper overall if you compare a decent ceiling fan with a proper air conditioner, especially since quality AC costs what it costs. Installing two units also isn't some huge expense - the extra you pay for the combined one already covers that.
A ceiling fan with built-in air conditioning is way more expensive than buying them separately, and that price difference rarely pays off. The built-in air conditioning tends to be less powerful than a dedicated unit, so if you really need to cool the space properly, it ends up not doing the job. Better strategy is to get a quality wall-mounted or split AC and use the fan just to circulate air on milder days, saving energy.
I don't think it's always more expensive that way if you consider the space - do you live in a small apartment? In that case, saving on the installation of two separate units and having just one on the ceiling might be worth it, even if the air conditioning is less powerful. Now, if you have the space and want proper climate control, then two separate units definitely work better.
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