Proponents of free weights would say that if you want to build muscle and lose fat, free weights is king. But if you would want the "streamlined" and refined-look, then machines would be best. There are other factors to consider, however. It's not just a matter of equipment, but it's also the poundage, the volume and rest periods that should be taken into consideration.
If you use a machine with sufficiently heavy load, say; 70-85% of 1 RM and do 3 sets of 12 with 1-2 minutes rest in between sets - then wouldn't it achieve the same result of hypertrophy comparable to that when using free weights?
I guess the real benefit of free weights, is the fact that it is unassisted and therefore it will challenge your balance, coordination and core more than machines that are considered: "self-spotting". Free weights also require more refined movements that would enable recruitment of stabilizers, synergists and antagonistic muscles to support and lift the desired weight.
The neural connections between the muscles, the brain and the perceived stimulus is also challenged. It's for this reason (and is common knowledge) that newbies who are merely starting to lift weights for 1-2 months, notice some improvements in terms of strength and to a certain extent - muscular size. This would usually plateau after the said time frame, thus the need for some variations in programming for continuous gains.
Since both machines and free weights are staple equipments in any gym, why not get the best of both worlds? You could either use free weights first, hitting the major muscles- then machines to exhaust those muscles or to focus on the smaller ones. The number of sets, repetitions and rest periods would depend on your goals, i.e muscular size, endurance, strength or muscle tone.
The most important thing to understand is the proper form, execution and breathing. Free weights? or machines? Use both in whatever order or use just one - it totally depends on your goals, how your body responds to it and how you feel at that time.
Keep the faith :)