If your choice is ONLY those two combinations, then I'd opt for the AMD set up.
Actually, I'd prefer the Intel Core I5-10400 for the newer chip set and integrated graphics, but I would not get that motherboard. Someone PLEASE tell me why ASUS, in this day and age, wastes two expansion slots on PCI; unless this is some sort of processor/chip set limitation on PCI Express lanes that I don't know about.
since you ask if they're my only companions, what else would you suggest in that reach budgetwise? It seems 10400/10500/10600 are nearly identical when it comes to gaming and most likely also in general use. the 3600x doesnt seem like that much an upgrade? the only one I could think of right now beside those two would be i5 9600k but I feel like its already getting "old"