Both methods have good sensitivity, but Taqman has a much higher specificity and allows multiplexing. I generally prefer Taqman, but Syber is cheaper...
Using the correct MIQE nomenclature, rt-PCR will be qPCR and probe-based methods such as TaqMan is more sensitive than intercalating dye-based method such as SYBR Green method to analyse gene expression.
Yogendra, keep in mind that the most important determinant of Ct value is the abundance of template. PCR is a doubling process, the more of the template, the earlier the Ct will be.
If you are working with samples that high high Cts (>30 Cycles), than a probe-based approach may push it back.
SYBR green based primer design can be just as effective as a probe at a small fraction of the cost.
Selected dye can not change the Ct value because Ct depends on the copy number of template not on dye chemistry. Both dyes have different chemistry and used for different purpose. Normally SYBR is used in large number of genes because its cheap and validation done by Taqman because its very specific.