If you run RAID 10 on a busy system and a disk fails, everything keeps running at full speed until you replace the missing disk and rebuild your redundancy.
If you run RAID 5 or 6 and a disk fails, suddenly every read operation becomes several times slower because the missing data must be computed from the parity and remaining data channels. If your normal day-to-day load on the storage is too high you are screwed until you rebuild your missing disk.
Write throughtput/latency on RAID10 remains consistent with previous numbers (latency perhaps milliseconds faster), but read latency and overall-throughput (as opposed to individual requests) will suffer on the mirror with the bad disk.
Recovery will drop read/write performance, depending on how fast you do it, but nowhere near as bad as RAID-5/6.
If you run RAID 5 or 6 and a disk fails, suddenly every read operation becomes several times slower because the missing data must be computed from the parity and remaining data channels. If your normal day-to-day load on the storage is too high you are screwed until you rebuild your missing disk.