Some of this has been stated before, but I think you have to consider the following:

What are your most likely destinations for business travel, and which of the three airlines serves these destinations the best?

What are your most desired destinations for award travel, and which airline serves them?

If you get only one match between the two, it is a slam-dunk.

Regarding the domestic business travel, also think about each airline's hubs. You will be connecting there often. For instance, AA and UA both use ORD, but, given the choice that you are faced with, I would not choose AA because I have had bad luck for years with their DFW hub: flight cancellations, system delays due to thunderstorms, denied upgrades, loooong walks, etc.

On the other hand, AA has it all over the other two with leisure travel destinations in the Caribbean. UA is stronger in Asia, both do a good job in Hawaii and Europe (including onward BA connections from AA), and so forth.

I would be surprised to find DL winding up a better choice than AA/UA for an EWR-based flyer. But if you were LGA-based, you could make an argument for DL.

You must have a great travel department &/or agency to offer you a choice of elite status on three airlines up front!