Is there any advantage of using methods using ATP measurement for cell viability studies compared to MTT assay?
MTT is a rather crude end-point assay to measure redox potential (and indirectly viability: live cells have a membrane potential and mitochondrial potential, high metabolic states result in mitochondrial biogenesis/enhanced activation, as does enhanced cell proliferation).
MTT has a small dynamic range ("window"), and its a terminal assay.
Fluorimetric ATP analyses allow for kinetic assays, and have a much larger dynamic range and sensitivity. Many of these assays can actually be conducted with labile mitochondrial potential dyes to get dual parameter kinetic + snapshot pictures of cell viability over time.
On the flip side, MTT is dirt cheap and only requires some patience and a basic spectrophotometer.