If you work in a field that requires precision (i.e. healthcare, manufacturing, engineering, etc.) then Lean Six Sigma may have more benefits to you due to the dependency on data gathering and monitoring any variation that occurs. This can be a very productive way to ensure the quality of your services and products. Through using DMAIC (Decide, Measure, Analyze, Improve, Control) each change inducted into a process is carefully monitored.
On the other hand, if your industry is more service-based or less precise, total quality management may work best for you in your situation. This means that you improve quality by having a purpose, erasing boundaries between divisions in the company, and ensure the training of every individual. Customer service might be an example where TQM is more appropriate than Lean Six Sigma.
Both methods are extremely effective at improving the quality of goods and services - if carefully implemented and supervised by a project management team.