The public beta is free, and comes a tiny bit after the developer beta, which isn't free.
If you want iOS10 and beat the rush, why not wait until after the release, rather than install a beta now and upgrade to a stable later (and having to wait until the rush is over).
I think the rush is a tiny bit of a myth. From all the upgrades I've done this year I've only had an issue once with their servers being unreachable.
Anyway, the difference is quite tiny. I don't think you'd actually be able to pick out 5 or 10 items that are so different you'd notice it.
Go for the public beta, and enjoy playing a bit earlier and getting familiar with it. If you find a bug though, report it 🙂