Personally, I like the 1st Mox Diamond over the 2nd Chrome Mox mainly due to pre-combo issues with Chrome Mox. I usually find that I rarely have dead cards in my hand, and I hate pitching cards that I want either as disruption or combo pieces (looking at you specifically Therapy/Thoughtseize) to yet ANOTHER Chrome Mox to make more mana. Mox Diamond is a more versatile mana piece, but has a slimmer selection of cards to pitch to it... however if I'm pitching 1 land for another mana source, then I don't feel as bad as needing to pitch disruption or business. The deck can function off of very few lands in play, so trading a land for a mox diamond doesn't seem to bad. Furthermore, Mox Diamond can't be wastelanded and can cast every spell in the deck, including Children.

The reason why I like the 1st Chrome Mox over the 1st Mox Diamond really just comes down to the amount of cards in the deck to pitch to them. Chrome Mox can actually do something pre-combo more often than Mox Diamond.

But, YMMV, and I can see why my argument for the 1st Chrome Mox can apply to the second one as well too. Test and find out your own preference. :)