In my experience, UA tends to have the lowest pricing when compared against NZ and SQ for the same itinerary (yes, any carrier can issue).

However, you may want to book through the carrier with the most segments on your itinerary since dealing with a non-issuing carrier in the case of any changes can be highly time consuming unless you memorize the fare code and know exactely whom to call and what to ask for.

I typically book on UA and fly SQ and NZ. UA only if no other D seats are available or if the connection beats other carriers by 3+ hours.