In fact, we ended up with me being in charge of "input" and him being in charge of "output". As in, I make the overall nutrition decisions, and when he became really worried about the chemical smell of disposable diapers, I did a little shopping to find ones we both could live with (he rejected the idea of cloth diapers), since I agreed the chemical smell probably indicated the presence of stuff our kid was better off not having in contact with his body 24/7, but wasn't as wound up about it as he was. He's also taking the lead on potty training, while I'm the one who's handling most of the execution of that because I'm the one on a part-time work schedule.
In that vein, when one parent cares about something VERY much, and the other kind of cares but not deeply, we've found it best to let the one who cares more have their way... as long as they're willing to do the extra work.
It also really, really helped that he was able to take a month off after our baby was born, and then the first month I was back at work after a year of maternity leave and our kid was starting daycare. This is available to all regular employees in Germany - 14 months of parental leave per child, to be split with at least 2 months to each parent, overlap allowed.
If you can at all swing it, time off that first month is critical if there's not a close relative or friend who will be living with you.