Aha! A thread I can answer

I've owned Mules and Riff Raffs for years, and I've just put Stormy Mondays into a Les Paul Traditional.
All mine are covered and unpotted.
I too think it's Riff Raffs for you.
My absolute favourite is suddenly the Stormies, but I've only had them for 24 hours so do take that with a pinch of salt.
I haven't had the Riff Raffs in a Les Paul so my comparisons aren't perfect (they're in an SG - a warmish sounding one), but here goes:
The Mules push the amp harder than the other two and feel "thicker". Mine are in a 335 but have been in a Les Paul. If it was the only guitar I had, I'd be happy with them, but it did take me a while to get used to Mules - I was expecting some sort of "holy grail" sound when I got them years ago, and was disappointed at first. When I'd got used to what they were giving me, I fell in love. BUT whichever guitar they're in has never been the go-to "let's do it" guitar - I always have to get into it for a while. I love my Mules, but I can see how someone might not get on with them as much as we all seem to...
Riff Raffs are brighter and harder edged and the neck is less "plummy" than the Mule neck. They also seem more expressive in my hands than the Mules. With the Mules, I'm playing the Mule sound, with the Riff Raffs I can bend them to my will a bit more. I played strats for years and years - so I'm used to getting 60s/70s rock out of single coils - I like guitars to be responsive to attack and guitar controls. The Mules are responsive, but I find the Riff Raffs to be more so. I love the middle position on Riff Raffs.
Stormies (and I'm still dialing them in heightwise) are bright but sweeter than the Riff Raffs. For me personally, it's a lot more pleasant bright - it's kinda my dream humbucker tone. When I want to get mean I can, when I want just good ole rock and roll but not too offensive it's easier to do than the Riff Raffs (I hit strings quite hard). The Stormies have the best string separation out of the three - open up all the controls and whack a barre chord, you can hear ALL the notes, both on bridge and neck. You can with Mules and Riff Raffs too (in comparison, say to 57 Classics), but then try it on the Stormies and you're thinking "hey! where were all these notes before?!!". But that's at the expense of output I'm guessing - they don't drive the amp as much. The thing is though, they're sounding just as "rock" with less apparent gain. For me, that's pretty much what I want... (I've been comparing the guitars for the last half hour, and I actually put the Muled 335 down with, umm, a "yuk!! too much"!!

- no wurries I'll get back to it!).
The other thing I love about how this Les Paul reacts to the Stormies is lowering the volume on the guitar - it goes all the way down with a usable tone. The Riff Raffs provide a "harder" clean sound when treated like this, which I find less attractive (but it does work well in mixes). I find the Mules can be a bit characterless when the guitar volume goes below about 4 or so. The Stormies I'm doodling with at the moment between typing sentences. I'm in the middle position, bridge on 2 and a bit, neck on 2 - and I could be playing a strat. Turn the volumes up, it doesn't get much louder, just more gain.
I've heard the Stormy bottom end is less defined... and I can hear this on the neck pickup on the bass strings. I think if you use much gain (I'm playing through something imitating a Marshall Bluesbreaker type amp running at full tilt, it is ok on this), but if you want clearly defined cutting bass notes from the neck with say late 70s gain, then you won't get them! You will from the bridge - it does squealy pinch-harmonic riffing best of the three (think Billy Gibbons). The Riff Raff neck, on the other hand, has always stayed tight for me...
SO - I think Riff Raffs. But if you have a leaning towards sweet rather than hard - Stormies might be it. If it was me, with what I know now, Stormies would be it... But I think Riff Raffs are the safer bet for you.