The most important thing when defining project scope is budget. The amount of capital a project team has access to directly impacts all processes of said project. Do we have the money to hire consultants for this specialized tooling we must create? Or do we need to spend the time/resources to educate our own employees to complete this task? Can we meet the customer needs within these budget constraints? Can we meet performance requirements with the materials we can buy with this budget? Does this budget even include a large enough profit margin to pay our bills? As much as we engineers don't like it, money is the lifeblood of our projects. A group with carte blanche can potentially complete a project faster, more effectively, or create a better product. However, creative teams can meet requirements within a tight budget. I have been in this camp before; more often than not my project teams have been under-funded. As such, we have had to scramble at times to make due with the budget we have. Life could have been much easier with a little more wiggle room.

When defining the project scope, the most important aspect is time. While I do agree with @hmara that the budget holds importance in ensuring there's wiggle room for the completion of the project, I think it would be more difficult to obtain that wiggle room with time. In defining the scope, milestones are outlined, setting deadlines for specific tasks to be achieved along the way to completion of the project. If there are delays in any phase of the project, this may cause the project to delay these milestones and potentially miss the deadline. A delay in one phase may lead to delays in the phases to follow, which could be detrimental to the timeline set forth in the scope statement agreed upon.

While I agree that the budget is crucial to the project, it can also be changed depending on the project needs and funding available. I believe the most important aspect of the scope is the project objectives and deliverables. They outline what the goals and basis of the project are and what the end result of the project should be. For the most part the objectives and deliverables stay relatively unchanged unless a change is approved by the team manager and other stakeholders. These aspects definitively establish what the stakeholders expect the manager to have complete at the end of the project and so all the decisions the manager makes throughout the project lifecycle has to be based on completing the objectives.