Ehh. Similar they are.
158 gr bullet. Check
Semi Wadcutter Check
Soft Lead Check
Standard Pressure 38 special Check
Those are standard pressure 38 bullets out of a 1 7/8" barrel. I think the OP is underestimating his velocity.
Not really trying to indicate equal performance, just that what he is asking about should penetrate at least that amount.
Um, that's pretty uninformed. Sorry.
1. The bullet weight is dead on for both, obviously.
2. If you can't understand the difference between SWC & SWCHP, you're going to have a tough time convincing anyone knowledgeable about reloading, hunting, or bullet casting that these two rounds are going to penetrate a similar amount. Hollowpoints (depending on the actual cavity geometry) may penetrate pretty much the same as SWC (small cavity gets jammed with cloth/sheetrock), or they may open up a great deal and penetrate much less (large cavity/flying ashtray style), again depending on what material they hit. There are a LOT of important variables when you talk about overall penetration that you are dismissing.
3. The Winchester loads may or may not be a "soft alloy". I tend to think that they probably are, but it's hard to say until someone more knowledgeable about this particular load's alloy jumps in. The BB rounds are a decidedly soft alloy (the reason they put a gas check on the back of it). Now, once you take bullet geometry into account, a VERY SOFT ALLOY LARGE CAVITY HOLLOWPOINT is probably going to mushroom quite a bit, and penetrate less than a solid SWC design, whether that SWC is a hard alloy or soft. If it's hard, then it won't even be any contest. The problem, though, is that this assumes that velocity is equal. Leading us to #4:
4. Pressure in both isn't going to exceed a certain amount, true, but PRESSURE HAS NOTHING TO DO WITH EXTERNAL BALLISTICS, other than it propels the bullet at a higher or lower velocity, but it's not a 1 to 1 conversion. Furthermore, cowboy loads tend to be WELL below on both pressure AND velocity. They are meant to punch holes in paper and knock down steel targets, not punch holes in living threats. The Buffalo Bore loads are designed specifically for a short barrel. The cowboy loads from Winchester are going to be designed for a longer barrel (i.e. a cowboy action style gun). Add to that the actual velocities that people are getting with this ammo, and that's a big difference (over 20%). We're talking about entirely different powders (BB uses a proprietary blended powder for their short barrel FBI loads), and loads that produce +p velocity in standard pressure vs a load that would be hard to even call warm, much less smoking hot.
Add it all up, and there's no way you can definitively call these two rounds similar, other than bullet weight and diameter, neither of which on its own will determine overpenetration. With so many variables,
It's possible (Likely) that BOTH will overpenetrate through several walls, so the OP needs to shoot straight to begin with. The only way to truly be sure is to do a box of truth style test.