I almost always sort myself out with flights, hotels etc. Went to the Maldives once and picked up a package, which is almost obligatory.
One of the benefits of a package is that you have minimal hassle when making the arrangements and you will certainly find some places that you would never have dreamt of arranging yourself.
Doing things yourself makes you feel a little more 'indipendent' I think. You can go where you want, when you want and how you want.
The DIY option can sometimes cost more and other times cost less. The economies of scale cannot be reached on your own, but some locations/agents have huge mark-ups, so you have to do your home-work, which is one of the drawbacks of the DIY option, I.e. that you have to dedicate a little time to making arrangements yourself, and getting them right, as there is no one to blame if you don't.