Just to clarify a couple of points:
Firstly, Star Alliance & IAG are not similar. IAG is the group which owns BA & several other airlines; Star Alliance is an alliance of a number of airlines, mostly under different ownership, which work together to offer codeshares on each others' flights. BA's equivalent is One World.
Secondly, Delta isn't a Star Alliance member (it's a Sky Team member) & doesn't fly MAN-EWR direct; I think you mean United!
Airline pricing is a very complicated business, but unless booking as a codeshare is significantly cheaper it's better to book with the operating airline - things such as seat selection can be difficult (edit: according to complaints on travel fora) if you book through a codeshare partner. As for cost, you need to balance the convenience & shorter overall travelling time of a direct flight against the lower cost of a one or more stop routing.
Edit: don't search for "cheap flights" - that can take you to some very dodgy so-called "Online Travel Agents" who don't have live pricing. Search onGoogle Flights & book direct with the airline.