Masters or PhD for quant HF

Hi, I'm recent Physics major graduate of Korea Univ waiting for graduate school admission.

Currently I'm accepted to Carnegie Mellon University Master in Computational Finance (CMU MSCF) and Columbia University Master in Operations Research (Columbia MSOR).

Here's a deal. If I go to CMU MSCF then I'll be working as a quant analyst (hopefully) after graduation, and if I go to Columbia MSOR I'll apply for PhD (high chance of acceptance since I got a chance to work with a phd student and a professor) and start working at quant hedge fund after that.

Both paths are find, but I'm not sure which path to go because I'm not aware of long-term consequences of my decision. On top of that, the fact that most of managing directors at quantitative hedge fund are PhD makes me feel that I have to pursue PhD as well. Lastly, if I'm not capable of independent research (PhD level), I have a fear that I would not be able to bring novel idea at some point

Bottom line is that should I go for only masters or go further (PhD) to become a successful quant at quantitative hedge fund (AQR, Citadel, Two Sigma, etc.).

Thank you so much for reading this long post.

P.s. Applying for PhD after few years of working experience would not be a realistic idea.