I do mostly panos with mfdb, and end up with pretty large files (25-50k pixels wide). When downsizing for web, I always do so in 3 50% increments. (I’ve built it all into some actions). The first step asks for a starting size which is my final desired size x 8 using “Fit Image” (so for a 1000px web jpeg I put in 8000). I then down size 50% using bicubic, 50% using bicubic sharper, then 50% with bicubic again. The final image usually gets a very low smart sharpen (91% at 0.3 pixel threshold), but this is decided visually with the image at 100% (200% on my retina display) and can be tweaked or skipped.
The idea came from Jack Flesher, and he tested quite a few different ways (when to use bicubic vs bicubic sharper). whether this gives me any better image than single downsize I don’t know, but seems to. Interestingly enough, even if the first fit image requires the file to be uprezzed the quality is still very good and maybe better than a single resize.