Bottle necks are not a big deal, but straight walled cases are a bit easier to work with, and they seem to last a little longer. Also, like I said, in a pinch you can use 30-30 brass to make cases for the 375 Winchester, and 30-30's are everywhere. Of course 444 brass is not hard to come by either, but it will cost you more than 30-30 brass. I'm just speculating upon the event that one were to completely run out of "headstamped" brass for either the 375 Winchester or the 375 JDJ.
I wouldn't mind having a big old 375JDJ! The 375 can take advantage of the heavier bullets because of the extra velocity. Of course with any gain like that, comes the extra punishment to the old shoulder, and for that matter, the pocket book. But like I've said, I've been eyeing me a 375JDJ also (after all, I already have a good bit of stuff to work with!). My old man has a bucketful of 444 brass that he's not using.
I'm just passing along my experiences with the 375 Winchester, and the experiences have been excellent.