MTT measures mitochondrial metabolic activity as a proxy for viable, metabolically active cells. A drop in MTT signal can reflect cell death, but it can also reflect a cytostatic effect, where cells stop dividing but stay alive. LDH measures enzyme release from cells with a damaged plasma membrane, so it signals lytic or necrotic death rather than a general drop in metabolic activity.
Neither assay alone tells you the mechanism of cell death. Add a caspase activity assay to detect regulated apoptotic death, since apoptotic cells can stay LDH-negative until late in the process. Combining MTT, LDH, and caspase readouts lets you distinguish cytostatic effects, lytic or necrotic death, and apoptosis with confidence.