OK, here goes...(sorry if this ends up a little long).
First - for the OP - you need to check out a few sites:
PRS Guitars | Electric Guitars, Acoustic Guitars, Amplifiers and Accessories
Official PRS Guitars Forum
http://www.vintagerocker.com/forum/forum.html
and
Electric Guitars, Acoustic Guitars, Amps, Accessories & more | Wildwood Guitars
Online Guitar Store
(no affiliation with the above stores other than being a thrilled customer of Wildwood; talk to Lance or Troy)
I use a Cu24 as my #1 now - and I was a Strat player for years, and still have a few. There are several PRS here, including two Cu24s. I have other instruments including Gibson, Fender, Ibanez, Parker. I reach for the PRS and Strats first.
There are a few key things to know.
Build quality on all PRS is superlative. I would buy any without having played it first, and have done so a few times, including both new and used guitars. There is "discussion" about whether the "pre-factory" guitars are better. While the very earliest production Cu24s (mid-80's) are more valuable, most people seem to agree that the guitars are as good or better than they have ever been.
There are multiple neck carves. At one time it was wide-thin, wide-fat, etc. Now they are pattern thin, pattern, pattern regular (I think that is correct). My Cu24's are both wide-thin but I have PRS with other necks. The only one I don't particularly like is the 513 neck, which is a special carve that is deeper than normal. At any rate, if you are sensitive to neck carves, consider that carefully before buying. I can say that a wide-thin does not feel as wide or thin as, say, a Parker Fly or Ibanez Satriani. Wide-fat to me feels closer to a 59 Les Paul carve; not identical, but closer.
There are multiple switch configurations, as pointed out above. Both my Cu24s are 5-way rotaries. This is the weakest spot in some ways because the rotary is just harder to switch, though it becomes easier with practice. "McCarty switching" puts a three-way toggle in place of the rotary and can be done as a conversion. To do this, the rotary switch hole has to be reamed slightly for the larger switch; but the rotary can still be put back afterward. Newer Cu24s come with 5-way blade switches. I wish mine had that. Rotary cannot be converted (at least not easily; maybe the PRS tech center (PTC) would do it, and put a second tone or volume in the leftover hole). Maybe I will trade some guitars to get the blade, but I love mine now.
There are multiple pickup configurations. The original was HFS (Hot Fat and Screams) for the bridge, and VB (Vintage Bass) for the neck. Both my Cu24s have this. I like the pickups generally, but would rather have either the 57/08 or 59/09 pickups (more vintage-sounding; do some reading on the PRS site and forum links above for more information). The VB is actually fine for me; the HFS, not so much.
If you're looking for something closer to your Les Paul, the PRS DGT (David Grisson Tremolo) model is the ticket. The one gripe you might have is that the DGT neck carve is narrow, and your technique needs to be clean. However, DGTs now come in other neck carves. They are only 22 fret necks.
Hope this helps.
Dave
PRS Custom 24 is always compared to a LP probably because of the glue neck. It sounds nothing like a LP. I own both. PRS sounds creamy and has amazing middle focused pickups. You can make the neck pickup sound like Slash, Santana and a Strat. Seriously. I own many guitars........ PRS is the best.
