So, if you speak to the team at Omnium and Bullitt, to them they are selling a completely different product with hugely different uses and therefore are not in any way comparable. To us in the UK I guess there's so few two wheeled cargo bikes around that we put them all in the same boat.
We sell Omniums to customers who want to carry 'things', faster than you would be able to deliver it in a car (this is true even in a small town like Bournemouth) we have a coffee roaster that delivers all their coffee locally (8 mile radius) on an Omnium. Omnium bikes are easier to store, considerably lighter and easier to handle when carrying a 'mid' weight item like tubs of coffee (50-60kg). They're also easier to carry weird shaped items as the 'flat bed' cargo style can have anything strapped to it. In Copenhagen they don't think twice about sticking a small child or two on the front of an Omnium, partly because they have huge cycle lanes and often they're being ridden by messengers/ex-messengers/experienced cyclists.
Bullitts are much more popular with people with kids, especially in Copenhagen, they're easier to just sling something into the front (providing you have side panels) knowing it won't fall out, including a child. We sell Bullitts to people wanting to ride along the seafront where it is extremely flat and there's not much traffic, they also offer a carbon belt drive option which is helpful when riding by the sea.
I have a Mini-Max because I can use it as a regular bike and it stands on it's end in my hallway. I don't have kids but I did have a dog who used to sit in the front of our shop Bullitt: