This is a very overlooked issue when starting a project.
I would first ask yourself how much time do I have to dedicate to managing the project?
If your time is limited or managing professionals makes you uncomfortable then it is VERY important to hire a full service contractor.
The second question to ask yourself is how qualified am I to be able to know if a subcontractor is preforming correctly?
There are so many carpenters, handy-men, plumbers and electricians out there, that knowing how to do the job correctly and efficiently will help you to save money and get the job done correctly the first time. If you are uncomfortable with questioning these professionals then a full service contractor help you to save money.
The third question is how large is the job?
if you are doing a small project you probably do not need a general contractor that will use sub-contractors to complete the job. In this case find the professional electrician, plumber etc. and verify their experience and work through previous customers.
Basically if you have time and willing to manage then you can completely do it yourself.
If you want it done without having to do anything but pick out colors then have a general or full service contractor do the project.
Either way you choose get multiple bids and remember the lowest bid is usually not the best. Determine what quality of work you want and go with whoever you are more comfortable with, remember this person is working in your home and you need to be able to trust them.