Well. I always believed it isn't make much difference accuracy wise. But some as to elevation .
But, I decided to do my own little test
First I got out a 357 and a 38 special as close to the same as I could
A 6" 19-3 which was finish worn but mechanically good and a decent 14-3
I also took along my home made Ransom rest which I have both K an N inserts for
Ammo, I have a pile of cast lead middle of the road 158gr SWC 38 specials. I don't load plain lead 357 much as if I am going to shoot a 357 it would be for "business" and even then a 357 isn't my choice for a "business" gun. So all I had were some fairly stout 158 gr JHP
Anyway fired a couple rounds out the 14, then took the grips off. Set it up in the rest and fired a cylinder full of the 158 gr SWC 38s at 20yds. Upper Left dot
Then I took it out of rest, fired a couple 357s from the 19 then set it up in the rest and fired a cylinder full of the JHP at the middle dot. Then,, I loaded it with the 158 gr 38 SWC and fired a cylinder full upper right dot
Here is what happened to the paper.
Interestingly the best group was the center one with JHP 357 from the 19
Hard to say there is much difference between the 2 38 SWC groups the 14 in upper left and the 19 in upper right.
All the groups were some what dependent on my 70 year old eyes without any glasses, that have been corrected by lasik in 1999, then by cataract surgery about 6 years ago and then a YAG laser capsulotomy this spring.
Certainly not enough difference in any of them to be noticeable with me shooting any of them even with a good 2 handed hold