I have two origins and I have not felt an SR3, so take this with a grain of salt.
One of the ways they save money on the origin is not having any options beside bolt handle and bolt face. No tang changes, no different magazine cuts, etc. If you want the standard tang and a BDL bottom, I would get the origin. I had one of mine opened up for a wyatts extended box and was still $350 under a TL3/SR3. Aesthetically I prefer the straight bolt handle, but its not worth the upcharge just for that.
Big Horn posted on facebook last month that going forward the Origin action would be machined from stainless instead of chrome moly. One less reason to pony up the additional money for the SR3, IMHO. The nitride finish on the Origin is very good and I can't imagine the SR3 being much smoother than this.
My advice, get the origin and put the $400 difference towards a better barrel, trigger, scope, stock, etc.
If you know what trigger you are using when you order, let them know and they will give you a different cocking piece to time the cock on close