Every software engagement starts with the same commercial question: a fixed price for a defined scope, or an hourly rate against an estimate. Clients often assume fixed bid is the safe choice because the number is known. The truth is that each model transfers risk in a different direction, and the right choice depends on how well the work is understood.
Fixed bid works when scope is genuinely nailed down: a defined migration, a specified integration, a rebuild of something that already exists. The vendor absorbs estimation risk, and in exchange the scope becomes a contract. That last part is what surprises people. Every change, however small, becomes a negotiation, because the vendor priced exactly what was written.
Time and materials fits work where discovery is part of the job: a new product, a legacy system nobody fully understands, anything where the requirements will improve as you learn. You pay for what is actually done and keep the freedom to change direction. The risk transfers to you, which is why it only works with weekly demos, transparent hours, and the standing right to stop.
Our own pattern is a hybrid: a small fixed-price discovery phase first, which produces the understanding that makes the follow-on estimate honest, then whichever model the newly clarified work calls for. Be wary of any vendor with only one answer to this question. The model should follow the work, not the sales pitch.