The '73 only has a problem if the ammo is too short (or too long, but that is not usually a problem and especially not with .38).
In the following picture, the stubby round on the left (90 grain bullet) is too short to feed in the '73 but the others feed fine. It has to do with the ramp on the front of the brass carrier block. Pettifogger has a nice tutorial online about how that works and how you can determine the needed length of your ammo, but I don't have that web address handy right now. But most cowboy ammo works fine.