I use negated searches a lot for tag gardening, but almost never use them alone, so that's not a feature I'd miss.
The only time I can think that I might use it that way would be to get two of the three ratings at once without an OR, say -rating:e to get safe and questionable. Even then I would rarely use it alone.
The only time I really make use of the numbered pagination is when skipping to the very end of a search query to work backwards. Working backwards makes sure you don't miss posts due to them shifting across page boundaries when you use tag scripts in conjunction with negated tag queries. I could learn to work around it though.
Like Glasnost said, order:id or order:date_asc is a good work-around if you simply want to browse in reverse post order. So that's probably not a feature I would miss a whole lot either.
I did sort of like the related tag counts on searches for general statistics on what the query returned, but if the new system only returns inaccurate (recent sample based) counts, it's probably not all that worth displaying.
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