It has nothing to do with performance. Well, I guess it does in a way. It all has to do with gear inches. A 12-25 10 speed will have a much lower range of gear inches. Also, the difference between each cog will be less. What this means you can get a better choice of gear for your cadence. When in the 16 tooth cog, it might be too hard to keep up your cadence and when in the 18 tooth cog pedaling at your cadence is too easy. So, if you had a 17 tooth cog, it would be perfect.

So, you might think having a cassette with each cog one tooth more than the next is ideal. Not necessarily, if you live in a hilly area, you will need a larger range of gear inches. Maybe a 30 tooth cog to get up the hill and an 11 tooth cog so you can fly down the hill.

If you are a professional racer, you don't need such a range, because you have very powerful legs and can easily ride up a mountain in a smaller cog. So a shorter range of gear inches is preferred.

The speeds of the cassette or freewheel really don't matter that much. It is the overall range that matters. If you have a 6 speed freewheel and a 10 speed cassette, with each being a 12-27, then your range is the same. What will change is having more cogs so you can get a closer match for your abilities. With the 6 speed, you might have a gear that is a little too hard and the next size is a little too easy. But it isn't that big of a deal. I have a few bikes, with a freewheel with 6 speeds, cassettes of 7,8 and 9 speeds. The gear inch range is about the same on each bike and I can ride any just as well. No real difference in performance because of the drivetrain.