I've attached an image from a spreadsheet comparing geometries which I put together last year when I was shopping for a new frameset. Comparing sizes 50-60cm, on average:
1. LHT chainstays are longer by 10mm.
2. LHT BB drop is 2mm shorter, so BB height is 2mm higher.
3. LHT standover height is higher by 24mm.
4. LHT heat tube length is shorter by 12mm.
5. LHT effective top tube length is longer by 4mm.
6. LHT head tube angle about the same.
7. LHT seat tube angle a little more slack in 58 and 60.
8. LHT wheelbase is longer by 14mm.
As tarwheel noted, the Saga does have a shorter TT and longer HT, which was also helpful in my case fit-wise.
The SO height difference was also advantageous for me, but I couldn't determine where they measured it (nor could CS from email/call I made). If they measure right in front of saddle, a steeper angled TT will indeed have more SO, but if measured near the HT it may actually have less SO. My mtb-based road bike's SO height varies by 3" depending on where I measure in the 15" of open TT between front of saddle and HT. I assume they measure in the center of the TT, which is usual convention.
The LHT has a 14mm longer wheelbase mostly due to longer CS and longer TT. Longer wheelbase is usually a good thing on a touring bike, as it's more stable. Since the Saga's chainstays (aka "rear center") are 10mm shorter than the LHT, the "front center" (distance from BB to front wheel axle) is 4mm shorter than a LHT. This means toe overlap (front of shoe or toe clip striking front tire or fender when wheel is turned sharply) is more likely on the Saga. Since I own a 56cm/700c Surly, and it has toe overlap with fender mounted, it is almost a certainty that toe overlap will occur on the Saga in size 56, where the front center is 6mm shorter than on the LHT.
At various times I've read the Saga won't take very large tires, despite the spec on their webpage. CS rep simply quoted the stupid website to me when I inquired, so no confidence from that conversation. I read/corresponded with three sources who claimed tire size was limited. I made a comment about it here @ bf.net and was once rebutted that the Saga did indeed accept 700x45s. Since there's no way I can inspect one physically I'm left relying on anecdote, so 3 say it won't take large tires, 1 says it will. I've wondered if this was an issue on early production models that was later remedied. Perhaps a Saga owner can weigh in on this subject.
The decals on the Saga are clear-coated-over, so you can't remove them like the LHT, but then hardly anyone would want to remove decals from Saga. Some LHT owners strip the decals for appearance sake.
The Saga has an oversized diameter head tube, which looks a little funny and makes me wonder why they used it. Obviously it's stiffer, but that's usually not an issue on a touring bike, even with longer HTs. I guess it's to simplify making the TT and DT joints, but all I know for sure is it makes the frameset heavier.
Surly apparently sells >10 LHTs for every Saga sold. I have to wonder how this affects quality of the frameset. Having owned a LHT and DT, I know the joint welds are as good as any steel bike anywhere. I don't know about the Saga - the few hi-res pics I've seen look like the welds are not as consistent as Surly (Maxway), but it's hard to tell without better pics or a frame in hand to inspect. The Saga claims it's made from a Tange Prestige, while Surly claims a generic 4130 (Prestige is also a 4130 alloy). If Saga is made from Tange Prestige, it is likely used only on the main triangle, with stays made from cheaper steel. I figure whatever unknown steel Maxway uses in Surly is also used when they make frames for Salsa, Jamis, Ritchey, Dawes, Greenspeed, Rans etc, so good enough for me. I have a 1991 Tange Prestige mtb frame, and it's nothing special to ride. I'm less concerned about the grade of 4130 used and more concerned about the strength of joints, placement of bosses, frame alignment, and the dozen other things that can go wrong. I don't know who makes Soma tigged frames, but their lugged frame is made by Maxway. Maxway of Taiwan has a great reputation, and they've been making the LHT for 10 years now, with only one year where they screwed anything up to any significant extent on the LHT, so this carried some weight in my decision.
You can buy a Saga for $425 or a LHT for $399, shipped, so the price is about the same.
British Racing Green is a good color for a bike or a roadster. I have to wonder if Surly didn't pick Super Dark Green after seeing the Saga with it's new not-purple paint job. Out of the 9 colors they've used on the LHT I only liked about 3 of them.
In the end I chose a 700c Surly Disc Trucker, partly because I like disc brakes, and partly because the 26" LHT I already had seemed like a great value to me. It was hard for me to choose the Saga even with fit advantages when there were unresolved issues, and I couldn't afford to risk my meager bike budget on a relatively unknown frame.