Research shows RG-8U has less loss. But, some comments were found about RG-213 being quieter (whatever that means).
What do you guys think is the best for an HF installation?
I don't know what research you've been looking at, but this is nonsense.
RG8/U and RG8A/U by definition are very long obsolete and no longer in production nor available from anyone. RG213/U is still current, and is the direct replacement for RG8A/U, but to a newer slash sheet of the military specification MIL-C-17.
A lot of "hobbyist" cables sold to hams, CBers, the commercial 2-way market, etc. are sold as RG8 "types" but aren't RG8/U. RG8X "mini-8" is a .240" O.D. "type," which really is nothing at all like RG8/U ever was. 8214, 9913, LMR400, 9086, 9096, 9913F7, LMR400UF and a zillion other lower-loss .405" O.D. cables are "RG8 types" simply because they are .0405" diameter (like RG8 or RG213) and are 50 Ohms nominal impedance. Other than those two similarities, none of them are anything like RG8/U, either.
If you want "mil spec" type stuff of this diameter, RG213/U or RG214/U are the current products. For "commercial/hobbyist" cables there are lower loss stuff, none of which is as rugged as RG213/U, but is perfectly suitable for our use. The lower-loss cables have air cell or "foam" dielectrics and fatter center conductors than RG8/U ever had, and as a result have lower loss, but they're still the same O.D.
Don't know what "quiet" means, but most of the low loss cables are double shielded, so they might have less radiation leakage than single shielded cables. It would take a very unique environment to notice that difference.