LBS MFA v. Vanderbilt MSF v. Work Experience in MC

Long-time lurker and first-time poster - Advice would be greatly appreciated!

I was recently accepted to both the LBS MFA and Vanderbilt MSF programs. I also have a full-time offer in management consulting (think Big 4 or similar). I am interested in pursuing a career in the short-term in MC with a long-term goal of ending in VC/PE (any size shop). With these goals in mind, would I be better suited to pursue a one-year master's degree at LBS or Vanderbilt or jump straight into work? An MBA is an option down the line. Ultimately, what path would provide me with the most opportunity in the short-term (Career Opportunities) and long-term (Career Opportunities and MBA)?

Background: Top 40 University (US) Very Strong extracurricular's Previous experience in AM GPA (3.5 - 3.75) and GMAT (700 - 720)

Thanks!