It depends. Sometimes it’s good, other times it isn’t. My girlfriend learned the hardway when I went first and flooded the objective area with Paratroopers, followed up by Crusaders, Halftracks and jeeps loaded with guys, etc. It was an uphill battle after that for her. Me going first gave me time to get my artillery (we play with hitched artillery in the beginning) and reenforcements up there by turn two and having only had faced 1 round of shooting.
So it depends. Sometimes it’s good and sometimes it’s worth waiting to see what your opponent does.
One idea we’ve been toying with is shuffling the unit cards (without looking), and that determines the order of initiative, so it’s a back and forth thing. We haven’t tried it yet.
-=Grim=-