We're booked on DL next month for the first time (awards). Friends that have flown both DL and UA have unanimously rated DL as their preferred airline between the 2 in economy. Separately to lounge access though, what you will have with UA over DL is priority boarding, additional baggage allowance and status printed on your boarding pass.
When Virgin announced the partnership was ending I considered booking on UA, but at A$6600pp return (economy) the DL awards flights won. Prices are crazy right now! I have managed to book my husband on UA in J class from Toronto back to Melbourne for A$6900, when the flight from LAX was $9800 if booked separately. DL was charging $22k for the same route... so... I hope you manage to find a good deal for your family
We flew QF earlier this year and it was over $4k each!