I switched to Sidebery a couple of months ago, and I find that it's somewhat better at restoring trees (though that could just be luck). I feel it's a bit more responsive, but these days I trim my tabs a bit more aggresive than I used to so my TST memories are somewhat biased.
I was surprised at how decent it converted TST tabs, but I can't remember how low my bar was; maybe try a new profile?
One thing I'm finding really nice in Sidebery though that TST can't do, is that I can create a parent node that is not attached to a specific page (via grouping).
Panels I'm undecided on. They seem useful, but they also seem like a bandaid over window management tools. One problem I'm having is that they don't restore, and all the tabs go back to the main panel. That may be some setting I toggled though.
Honestly, I don't remember. A year ago when I was considering going back to vertical tabs, I read a bunch of discussion thread and articles, and got the impression Sideberry might be better. Tried it, and it resonates with me - unlike TST, which I tried and quickly abandoned several times over the year.
Can't really point to any concrete issue, other than I have a distinct feeling Sideberry is much faster/lighter, and feels more like part of Firefox vs. some bunch of JS faking an UI on top of it. Sorry I can't give you a more objective comparison. I did find this though:
