By "more skills" I assume you mean the number of skills, or number of different skills.

In that case, I'd say : Manager, assuming we're talking about a good manager or good engineer.

The Manager needs to understand the technical/engineering enough to evaluate the engineer (either a simple performance appraisal or just keeping the engineer from b^ll&hitting the manager.

The manager also needs to understand the politics (yuck!) and have the people skills to know how to motivate and inspire the engineer.

In short, the manager has a broader range of tasks to perform (technical, political, interpersonal).

This is not to sat the manager is more or less important than the engineer, just that it takes more (and varied) skills.

As they say, those who can't do, teach, or in this case, manager. I would definitely give the skill to the engineer, but that's not to say that managers are without skill. I would call the good ones "resourceful" or even "wise."

Technical skills, engineer. People management skills, manager.

It really depends on what skills you are talking about.

Both Engineer and a Manager have skills depending on their workplace and work , they are assigned. They both should have Technology and Human Skills.

An Engineer should not only have good technical skills, but some Human skills also. and vice versa is also true.

A business runs like a clock-work, professionals are like individual gears that tightly bites along with each other.

In my opinion, it is not fair calling a profession is more important or requires more skills than another.

The correct question you should ask yourself is "Is my business more profitable if I focus my resources on engineer roles or management roles?". I think that will be a valid question and answer will depends on the natural of your business.