I am having a little difficulty with the first part of your question. When you say " I have them or some older Winchester....." what is the "them" you are speaking of? There isn't enough info to specify what you are trying to compare.
I am assuming you have a .357 magnum handgun but are just looking for a good load that is cheap to shoot in it, be it .38 or .357, correct? If so you have lots of choices. If your goal is just quality and accuracy, then you might want to try some .38 special round nose lead, semi wadcutters, or 158 gr lead HP +P's for a little more zip. If you like shooting the hotter magnum loads, you might look at the 110 gr Winchester USA .357 HP's. These are hotter than .38 loads but are still more mild on the shooter than the full power 125 gr loads. Otherwise the American Eagle ammo you mention should be good stuff. However, I wouldn't necessarily recommend most of the above loads for defensive use.
And before I go let me give you a word of caution about using .38 special full wadcutters in a .357. While you can shoot most .38's in a .357 without any problem at all, the full wadcutters can be a bit dangerous because lead shavings from the bullets have been known to hit a few people standing beside the shooter. I wouldn't recommend these unless using them in a .38 special specifically.
-Charging Handle