First of all, a BIG Thank You Hannes for your hard work to improve com_finder and for trying to move Joomla search to something better.
Would there be a way to offer the best of both worlds to websites ?
Most websites have only one searchbox.
In Joomla's case, the site admin must make a though choice, depending of his use-case, website and extensions used.
Both methods offer advantages and disadvantages, depending on extension.
E.g. for content, the new finder advanced search method is probably almost always better. For some other extensions, the old simple search method makes just more sense.
Even have a marketable name suggestion: "Unified Search".
That could comprise simple search (for activated plugins only), advanced search (for activated plugins only) and let's try to imagine extensibility and general API: possibly third party search methods.
By default, in new 4.0 installations, for core stuff, we could activate advance search for core extensions that are perfectly ready and by default use unified search in frontend.
That's just an idea. I have not done any research on that, nor verified if someone already proposed it . So, sorry if that's the case.
Best regards to all and kudos for all the cool advances and great work on all fronts!