These two models are very popular in the desert southwest for locating Couse deer, Desert Big Horn and Mule deer. I've spent countless hours on the tripod behind all three renditions of the 15X56 and currently own the HD model. I've also spent a good number of hours behind the 12x50SV but don't own it.
The SV provides more of a wow factor where overall image is concerned, is slightly brighter where overall image is concerned and is far more usable as a hand held.
The biggest advantage for the 15X56HD is that it resolves more detail and does so with an overall image quality that isn't far behind the SV. This applies only to the HD version however. I owned the 15x56neu alongside the 15x56HD for about a year and took them out frequently for comparisons. The more outings I had with them, the more obvious the differences became, with notable advantages going to the HD model.
I find the 15x almost useless while handheld, even with my elbows supported on the hood or roof of a vehicle because roughly 85% animal acquisition on distant terrain relies on their movement. The severity of shake, even from my heartbeat at 15x makes seeing animal movement almost impossible. It's still difficult at 12x but it doesn't seem ridiculous like it does with the 15x's.
I think the choice will come down to the ratio of handheld vs tripod mounted viewing first and resolving power second. If you're going to use this binocular handheld for even 10% of the time, I'd say go with the SV's. If you're going to use this binocular 95% of the time tripod mounted and need to resolve very fine details, especially in low light, the 15x56HD's will be the better choice.
As a final note. I usually go into the field with two optic combinations when searching and studying animals. I'll pair the 8x32SV & 15x56HD when long periods of tripod use are expected and I'll use the Canon 10x42is & 15x56HD when I expect to be on the move, traveling from ridge to ridge, covering ground and viewing on the go.
In a pinch, I can still use the 8x32SV from a standing tripod while on the move. These days however, I prefer to the keep the tripod stowed and use the 10x42is offhand and then get out the tripod with the 15x56's when needed.
Hope that helps some!