The Solid-State Disk (SSD) should have faster read and write times than the Hard Disk Drive (HDD). It is a smaller disk (as would be expected), but 128GB is plenty for installing an operating system such as Ubuntu.
If you do not want any other operating system installed in parallel with Ubuntu (a Dual Boot system), then using Erase Disk and install Ubuntu onto the 128GB SSD would result in a faster boot sequence than installing on the 1TB HDD. If that is the sort of performance you are looking for, then that should be pretty straight-forward.
The 1TB HDD could be mounted on a suitable directory as a data disk if you need to store lots of large datafiles (movies, large databases, etc.)
Without knowing what you want to use it for, it is hard to give detailed recommendations about "best performance". Do you do use programs that do lots of disk access? Lots of internet access? Lots of calculations in memory? Each of those use-cases has different requirements to give "best performance". I've tried to show what my assumptions are when providing options in this answer. I hope this helps :-)