As for history, imagine you're researching a topic and have gone through fifteen search results, decided three of them were relevant, and closed the others. Your history is polluted with all fifteen, whereas this tab search will directly return you these most relevant pages only.
I hardly use it, though, because I usually have < 100 open tabs, not thousands like others have. I identify tabs by their tree structures (parents, children, siblings tabs) and the prefixes of the titles, whose lengths don't depend on how many tabs opened, because the tabs are arranged vertically.
Fortunately, I also habituated the simple behavior of "If I realize I have a lot of HN tabs open, right-click and close the entire pane". That's how I know I'm clocking about 100 tabs per two days on HN alone.
Also, Sideberry changed my tab hoarding habit in a way that still results in keeping hundreds of tabs, but using them in much more sensible way. I keep them arranged in trees stemming from topical groups on high-level panels, and trim or kill as they're no longer useful. Most of those tabs are unloaded anyway, but the interface works as excellent short-term (days to weeks, sometimes a few months) bookmarking system - and I don't lose tabs anymore (as in knowing the tab is there somewhere, but not being able to find it in the vast sea of other tabs).
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:
https://old.reddit.com/r/firefox/comments/118ddge/tab_manage...
which is a recent(ish) discussion, and the points made there seem accurate.
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.
Except for the annoying interaction (I think) with "open new tabs next to current tab", which causes Sideberry to somehow leave behind lots of stupid empty tabs named after the page the real new tab had. I deal with it, but it's annoying.
You can save all of the tabs of your current session as a bookmark folder in one fell swoop! Your research tabs can be all saved together and opened as a group! Your gift ideas that you won't close because you don't want to forget about them can be saved in a folder named gift ideas so the next time you need them you have them, without the cost of using up your extra RAM and CPU cycles!
I remember both Chrome and FF making a big deal over that point years ago.
For games, I often have a bunch of wiki tabs open at the same time.