When my LM1000 came to me it had the 16" front wheel and was shod with Metzelers (15 years ago, and the tires weren't new) The front end felt totally untrustworthy. After reading a lot of anecdotes, I swapped on a 18" LM3 wheel, with new Metzelers. The front then was extremely stable, but heavy and slow. I ran through 3 sets of tires subsequently, Metzeler x2 and most liked Michelin Pilots. But where it all went right, was while restoring it I put the 16" front back on, added longer rear shocks, dropped the forks in the trees 1/2" and it turned magical wearing Pirelli Road Demons. The Mille GT is wearing some Shinkos, or other no-name tires; they're old, a bit scary looking but not worn. They are very neutral handlers on that bike, with only the slightest tip-in in turns.
I do recall on the LM that when the rear center wore, it tended to drift on fast straight roads (which are all I have at home)
I always tend to 'sticky' tires, because I imagine I'll go ride some nice roads far more than I actually have opportunity.
I think the Tonti is less affected by the profile than the geometry- 'feeling the difference' is not the same big change as setting the geometry correctly. But you *can* feel the difference, where I really never noticed on the Asian bikes I had. The Sport-i is far more sensitive to tire profile than the Tonti, which is a function of tire width probably.
FWIW, the Mille GT will get Michelin Pilots if they're still available when the time comes.
*the above statements are not paid endorsements, nor are the opinions expressed valid beyond the skull of the author*