Both methods use the same enzyme, the method of generating and quantifying signal is different. SYBR Green is more inexpensive and easier to design (one fewer oligo to worry about), but more prone to false positive signals (primer dimers and non-specific binding) than is TaqMan. TaqMan is more expensive than SYBR Green, but is more specific. Mitigating the harder set-up, many targets are sold as kits from multiple sources (obviously human is most represented).

Long version of saying, 'it depends what you need.' If you have a well designed primer-set with minimal cross-reactivities, SYBR is just fine. A target that is more promiscuous will likely be better seen using TaqMan.

Good luck.

TaqMan is more specfic as Matthew suggested but its very expensive if your primer is fine and its not forming dimer then SYBR is best to use for Real time PCR.