Don't forget the SWACs fangirls. Wherever they are.
Anyway, just because you have to assume that SWACS have superior radar, doesn't mean it's true. I already mentioned that carrier radars are limited in range because of LoS issues with the horizon... at sea level, the range isn't going to be more than about 20 nm, maybe slightly more with over-the-horizon capability. There's no practical benefit to outfitting a carrier with superior radar; in any case, a carrier's escorts (both airborne and seaborne) can help extend that range considerably.
I would think a big capital ship with a huge power plant would be able to mount a big honkin' radar at a minimal additional cost. It's also fairly obvious that SWACS are not used routinely in the WC games in any sort of close support role to carriers. As for whether radar arrays have to be obvious, if you look at the phased array systems on AEGIS ships, they're not obvious, either: just flat areas covered with hundreds of brick-like transceivers. That makes just about any area of the very-angular Midway an appropriate spot to put a radar. Note that the superstructure extends both well above and well below the hangar "wings" (for lack of a better term). This should eliminate the problem of the "wings" blocking radar coverage from one side. This aspect of the design might then suggest that the Midway does have sophisticated radar. Then there's that big thing sticking out the back; I always thought it looked kinda silly. I think it's supposed to be used by the science team, but this also suggests the possibility that it might be equipped with special sensors used for scientific data collection (I mean, why else is it so freak'n huge?); it might even be a radome of some sort.
The fact of the matter is, the only directly destroyable structures in Prophecy-era phase shielded capital ships are shield emitters and weapon turrets. The weapon turrets need to be on the outside, because you can't seem to beam lethal energy and missiles through phase shields (makes sense). Everything else is protected by the phase shields. There's no reason to think that the radar should be any different; heck, maybe you could incorporate radar into the phase shield generators themselves. Communications can clearly be transmitted through phase shields, but there are no obvious communication arrays, either.
Unfortunately, the game designers didn't seem to give the idea of "blinding" capital ships much thought (even blowing up the bridge doesn't seem to have much effect; I flew a number of missions with the Cerberus's bridge supposedly blown to kingdom come--die, Enoch, die!), so we really don't have any idea whether or not ships mounted sensors at all. I think it's obvious that such ships needed radar, even if just for navigational purposes, so the likely conclusion is that the radar just simply wasn't vulnerable (like, strangely, the hull--the most disappointing part of the WCP/SO engine was the fact that capital ships wouldn't blow apart, no matter how many nukes you dropped on them). The HARM missiles were for use against the weapon turrets (although I think they pretty much sucked at that role; my HARMs always ran into some part of those damned angular alien capships--I kept hoping they'd skim along the surface and hit them from the side, instead of going directly through as much armor plate as possible); I'm thinking that turrets had their own fire control radar (like the Phalanx CIWS), perhaps in case central coordination broke down, or just for terminal guidance.
I don't think the technical feasability of mounting sophisticated radar on cap ships is any obstacle. What we then need to consider is whether it's tactically advisable to put sophisticated radar on capital ships, or use any such installations routinely. The Midway, designed for independent action, would probably integrate sophisticated radar, while maybe older carriers would not (however, I'd think otherwise, since in many cases in the games, we're stuck on carriers operating independently). The Plunketts are one of the few ships that has a rotating radar (as ridiculous as mechanical scan 6 centuries in the future might be), so maybe this indicates that the Plunketts were designed with sophisticated radar (perhaps in line with their long range engagement mission).
The main argument against using active radar on a capital ship is that it puts a big flashing "kick me" sign on the battle group. Thus you'd probably want to keep active broadcasters on the less valuable ships, like destroyers, and most of the time you'd use passive radar; this is, in fact, how it's largely done today, and it would make sense in the future as well. However, I don't think this necessarily indicates that the radar on cap ships would be inferior to an SWACS; given the high value of capital ships, I'd say you'd want to have the best radar available, just for emergencies alone. After all, you can afford to lose any number of SWACS, but if the carrier goes up in smoke, well, you're royally screwed over. And contrawise, there's no point to having 4 SWACS if your carrier goes up, so might as well put all your eggs in one basket.
Now, with all that said, please let me repeat that I am not opposed to SWACS. Even if the radar range on the carrier is 1,000,000 km, an SWACS with a range of 100,000 km is still valuable, because you can fly it out a million klicks and extend the range to 1.1 million km, or patrol an asteroid field looking for hidden craft, or coordinate actions far from the carrier, or whatever. However, I think the high value of the capital craft argues strongly that you'd want to put the best radar feasible on such ships (mainly as a defensive measure, not really offensive), and I think the size of cap ships argue that they'd be inevitably superior to what you could mount on an SWACS. And, as I argued before, it'd be rather lame gameplay-wise to force you to park an SWACS in the center of your battle group, simply because the radar range exceeded that of a carrier (not to mention it'd help to pinpoint your position just as well as putting the same radar on a carrier). Better to focus on the mobility and expendability of SWACS, rather than the superiority of their sensor suite.
So, in conclusion, SWACS are good for offense, but I think their defensive suitability is more limited.