I prefer random under the tree with me handing them out for kids to open in turn and they see who gifts are from. Kids are really well behaved and ooh and ahhh and patiently wait their random turn.
DP prefers separate piles around the living room so kids run in, open all at the same time...no one knows who the gift is from...
I say if separate they will be disappointed before they've even started opening them if their pile is smaller.
Fyi we have a couple of kids each and this is our first Christmas together. He's always done it his way. I've always done it my way. Kids are mid teens to primary age.