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Reputation along with financial backing would decide who would pull the contract. Most likely Bruce Wayne according to "statistics":

According to Forbes 25 largest fictional companies Wayne Enterprises had an estimated sales of $31.3 billion.
According to Forbes 25 largest fictional companies Stark Industries had an estimated sales of $20.3 billion
Stark Industries focuses mainly on weapons development, while Wayne Enterprises produces many products from pharmaceuticals to weapons. Both companies hold many government contracts.

According to Forbes Richest Fictional Characters,
Bruce Wayne is worth 7 billion.
Tony Stark is worth 6 billion.