Happy to jump in with my experience here. I bought a 4ohm SL212 to go with my TH500. It looked like the perfect match by the specs. I then played it for awhile and sold the SL212. I loved the recessed handles of the SL212 vs the idiotic straps of the SL112, but that's about it.
I did some digging before I bought the 212 and I chose to disregard all the folks who were saying things like "I love SL112s, but for some reason this SL212 doesn't sound like two SL112s in a single box." I don't know what is happening technically, but the SL212 just does not have the same punch and definition of the SL112 cabs. It's just a deep, woofy, undefined, bassy blob of sound that comes out of that thing. It sounded its best when paired with my GK Legacy 800 amp and a really sharp, cutting bass. Even then, it sounded like there was just a lot missing in the upper midrange. Plenty of tweeter, etc going on, but not much in that 1-2khz range.
To be able to hear myself with the band at church I really had to push a lot of volume. Then it was overbearing and exhausting. I gave that cab two weekends there, then brought it back home and sold it. I took my Mesa Subway 115 in its place and it was just awesome! However, I like my Mesa stuff a lot and play it at home regularly... didn't want to leave it at church or schlep it back and forth every Sunday.
I soon replaced the SL212 with 2x GK Neo 112 II cabs and have been very happy with them.
Gallien-Krueger Neo 112-II 1x12" 400-watt Neo Cabinet with Horn 8-Ohm | Sweetwater That was about 6 months ago and I am still impressed with how effortlessly great and powerful they sound. And they're light! Under 30 lbs each. I got a good deal on them from my SW dude. Just over $800 for the pair, brand new. I am just as happy with this stack as I am with the single Subway 115, and I actually got both of these GKs for less than the single Subway cab. Now, I still prefer the Subway 115/210 stack over the GK 2x112 stack, but for leaving-at-church-duty, I am absolutely happy with the GKs.
The GK stuff is definitely more open/livelier than the Aggie SL cabs. I personally think the Aggie stuff is pretty overpriced now. They took a huge price increase towards the end of last year. They were just a touch less than the Mesa stuff at that point. I bought mine when the SL212 was $1149, I think, and my TH700 when it was selling for around $700. Now the TH500 is $900! They've leapfrogged past Mesa in price and the GK stuff is a bargain, comparatively. I blame the Korg buyout for trying to "cash in" with no real new innovation to justify the hike. I do NOT feel like Aggie is putting out a higher quality or more innovative product than Mesa to warrant their prices these days. I wonder if we'll see a price drop on Aggie in a few months, like Ashdown seems to be doing now. Ashdown went berserk on their amp prices last fall, and then last week I started see "price drop" notifications coming through on some of their Evo heads.
The tonal goals of each brand are vastly different from each other, but I'm not trying to nail anyone else's sound specifically... just find what works for me. Aside from the SL212 cab, I'm able to twist a few knobs and get sounds I like from all three bands pretty easily. I also really like to mix 'n match the stuff as well.
Sorry for the book. I hope you find a good deal on cabs that will make you happy!