While I've never heard the KH310, I do own the JBL 308p MKII. A month ago or so I used my parents as blind listening test participants to help me decide which speakers I wanted to use in my home office. Main contenders were Revel M105 and Genelec 8030c, but I threw the 308p in as third candidate as that's what's recommended by Toole. 4 subwoofers were used to equalize the low end. Overall order of preference was 8030c > M105 > 308p. The gap between the M105 and the 308p was larger than the gap between the 8030c and the M105. 308p did have the -2 treble switched engaged as this was back before Amir measured them, and back when I thought they measured like the 305p. My best guess is that huge distortion spike right in the worse place it could be(most sensitive portion of the midrange) is likely the cause of them being less preferred.
Based on that, I have a hard time believing the 308p would compete well with the KH310. I know I'd certainly rather own the KH310 than either the 8030c or M105
. My belief is that the Olive score is probably overrating the 308p a bit(due to not considering distortion), while at the same time underrating the KH310 a bit. My guess is there'd likely be a much bigger gap in a level matched blind test than the Olive score would suggest, and when then factoring in the KH310's much superior dynamic capabilities, I'm certain it's a much better overall loudspeaker.
I would argue that the 308p is the better value speaker, but that's a different argument, and it has an advantage there, being the cheaper of the two.