I do have a physical copy of the fabled third edition, and while it's a beautiful book, I prefer the 2nd edition rules because they are less crunchy. BESM2 was the pennacle of Tri-Stat development because it provides a lot of options with little number crunching, while still running like a "traditional" RPG. The third editon is more like a "roll-over" version of Silver Aged Sentinels. The one "stock-genre" of anime the BESM2 doesn't run well out of the box is pet monster, but there is a supplement here on rpgnow for that. If you buy this pdf, I suggest geting the Fantasy Beastiary, Cold Hands, Dark Hearts, and maybe Space Fantasy, but really, with the core book, you should be able to run what you want.
[5 of 5 Stars!]