Well, as usual, Sheldon covered it:

"If you install an ISO crank on a J.I.S. spindle, it will sit about 4.5 mm farther out than it would on an ISO spindle of the same length.

Confersely, if you install a J.I.S. crank on an ISO spindle, it will wind up about 4.5 mm farther in than it would on a J.I.S spindle of the same length.

Theoretically, ISO cranks should only be used on ISO spindles, and J.I.S. cranks only on J.I.S. spindles.

In practice, you can very often get away with mixing these sizes, as long as you select a spindle length that gives the desired chainline.

Taper matching was fairly important back in the day of loose-ball cup-and-cone bottom brackets, because these required regular maintenance/overhauls, and this required removal of the cranks. Every time you remove and re-install a square taper crank, the hole in the crank is liable to get very slightly larger.

This was particularly an issue when using J.I.S. cranks on ISO spindles, because over time, as the crank went on farther and farther, you could run out of taper, and the square end of the spindle would become flush with the surface the crank fixing bolt/washer pushed against. At that point, further tightening of the bolt won't make the crank any tighter, since the bolt is bumping onto the end of the spindle.

These days, however, most folks are using sealed cartridge bearing bottom brackets. With these, there is no routine maintenance required, so typically the crank will be installed once, and will stay in place unless/until the bottom bracket needs to be replaced. This greatly reduces problems of wear to the interface.

I generally avoid mixing sizes on customers' bikes, but I have a lot of experience mixing ISO/J.I.S. in both directions on my own personal bikes, and it as never given me a lick of trouble. "

From:
http://sheldonbrown.com/bbtaper.html

So there it is. They both work with each other. Pretty much. I'm going to stick with the 600 (JIS) crankarms on the ISO spindle 'cause it looks like it'll work pretty well as it sits pretty far on the spindle but with plenty of room before bottoming out. I think. We'll see after some miles and fixxy trix (just kidding).

Oh, and there's this, also on the same page:

"(Note: Old Ofmega/Avocet spindles were quite a bit skinnier/longer even than ISO. There are no modern bottom brackets that work with old Ofmega/Avocet cranks.)"

So, Komissar, you might be SOL if the BB your cranks are old Ofmega and your BB is new Ofmega.