I have a little experience with the smaller Tannoys and also own the 4367. I feel tannoy would be a backwards move for me. I think point sources are a bit over rated (having owned a few) if you sit in a tweaked out sweet spot. The advantage is the vertical dispersion is even and if you just sit down that is often accounted for with good speakers designs. Keep in mind the JBL is a “point source” from 700hz up where it matters.
There are two places I feel the JBL 4367s could be improved. The deep bass and soundstage width/depth. The bass is easily fixable and improved with subs. I have a few threads on using sub with my 4367s if you are interested you could look them up under my profile.
If I were looking for something different I would target a wide dispersion speaker for more of a room sound and less controlled directivity you get from JBL. This would focus on the short coming of the JBLs with a wider and deeper soundstage.