I'd say it's possible the composition and hence performance is different, but I don't think that's the only factor. Where I work (at a commercial joinery making windows, doors etc.) we go through thousands and thousands of screws per month and I can tell you that 99% of the screws that you get are rubbish - just generally poor quality, easy to snap, soft heads which round out etc. and even screws which claim to be made from the same stuff, by different makers, can vary wildly in terms of performance.
Generally I would say if you find one make of screws which works for you, then stick with it. Even if the material composition is the same, I believe things such as heat treatment/how they are formed can affect the performance. I'm no metallurgist but cold-forged screws seem to be better for at least some alloys as I think the metal "work-hardens" and becomes stronger through the forming process.
If you're looking for good strong screws then I recommend Reisser R2's if you can get them, but these are not "pretty" screws which you might want to leave on show. They are super super strong through - hard to round out and they almost never snap unless you screw in and remove the same screw repeatedly.