I find TN660 crispier feeling and much stiffer than BG66UM.
If comparisons are possible TN660 and TN680 are "YY Nanogy like" strings but with harder feeling.
During restringing it seems you are dealing with a metal wire.
They can take high tensions, I ve once applied TN660 @ 31 lbs without problem.
About TN680 (gauge 0,68mm) my review is the same.
About HTR Ive never used it.