[mikestar]

Prefer weak 2♦ vs. anything (unless 2♦ is absolutely necessary to plug a hole in an otherwise good system. Note that the Precision 2♦ is not needed--the 1/4 of 1% of the time you are 4-4-1-4 you just open 1♥).

Garazzo refused to play multi as he was unwilling to give up the "best preempt in the game": the raise of a weak 2♠ to 3♠.

[Antoine Fourrière]

I prefer the very European multi (preferably without the strong option, although it is quite playable that way) to the very American weak two in diamonds. Of course, like others said, the acid test is how you play 2♥ and 2♠. (It may be of interest that Zia and Rosenberg, who have a long bridge playing experience on both sides of the Atlantic, have decided to retain both the multi (as a weaker option) and the natural weak two.)
IMO, the multi loses big to the natural weak two with spades (I completely agree with Garozzo's comment, and I think that even the Poles would benefit from opening 2♠ indifferently with AQ9542 632 K7 98 and with KJ652 4 87 KJT74), but gains (not as much) with hearts, and there is something to be said for playing 2♠ as weak, but 2♦ as either a weak two in hearts or one or two bothering hand types.
I also find interesting the 2♦ weak in diamonds or hearts played by Liggins and Fawcett as described in this month's Challenge the Champs, but I have no definitive opinion about it. It nevertheless seems wiser than the 2♥ weak in hearts or spades which is played (usually NV) by some European pairs. (True, a 2♥ which would be weak in hearts or weaker in spades may offer some protection when responder has to pass with a misfit for hearts and opener has in fact spades, and doesn't prevent you from opening 2♠ with a respectable hand.)

As for the 2♦ Precision opening, I'm sure it should cover other hand types, but I'm much less sure which.