If you have hardware raid then you'll most probably have a hardware controller with hardware cache on it. If that controller has a BBU (battery that retains the contents of the cache on power loss) then the performance difference will be huge.
Having cache with BBU will speed up most of you things a lot. That's because all disk syncs/fsyncs will be instant, meaning that all disk changes for databases, syslog, filesystem journal, etc will be much much faster and won't need to flush the whole write cache to disk.
Having said that, the above is because of the BBUed cache. I.e. the performance should be equally good if you implement software raid on top of the hardware RAID controller. I.e. if you decide to do SW raid when having a HW raid controller.
Regarding their differences, HW raid is usually hassle free and usually comes with hot-swap-ability. You'll have to test that yourself with SW raid as the underlying hardware may have issues.
AFAIC (and I'm propagating some rumors here) HW raid manufactures dedicate a lot on this and take into consideration disk manufacturers and even specific disk models. They are implementing a number of hacks to overcome issues with disks, both for performance and reliability. On the other hand, SW raid will be always improving with kernel upgrades while OTOH it has been said a number of times that HW raid firmware is really bad.
Finally, HW raid comes usually with some logging meaning that you can look at the logs to figure out if a disk is misbehaving. Then again on SW raid you can just run dmesg or look at syslog.