Having seen these contracts in action on a smaller scale, time and materials works great if there is continuous delivery. If you're not getting value for your money, you can identify it earlier and cut your losses.
If you do a firm fixed price contract, the contractor takes on all the risk and will charge a much higher price to compensate. You'll also spend a lot more time and energy on writing bulletproof contracts because the stakes are so much higher. Worse, you'll need to do contract negotiations for every requirements change.
It's possible to make either work, though. I don't think using a different contract type would have fixed the root problem here.
If you do a firm fixed price contract, the contractor takes on all the risk and will charge a much higher price to compensate. You'll also spend a lot more time and energy on writing bulletproof contracts because the stakes are so much higher. Worse, you'll need to do contract negotiations for every requirements change.
It's possible to make either work, though. I don't think using a different contract type would have fixed the root problem here.