Should I choose industry internship or research assistant job at the lab? Currently, I'm a CS master student and I want to apply for a PhD program in the coming Fall. I'm interested in the system research (i.e., distributed system).

Right now, I have two opportunities presented in front of me:


Go to a professor's research lab over the summer. The professor's interest is in distributed storage and that quite matches with my interest.


Pros: Work with a professor directly
Cons: there isn't much pay and I want to rely on myself financially instead of family.

Do a software internship with High-Performance Computing (HPC) Infrastructure.


Pros: Good pay and industry experience that relates to my interest (HPC infrastructure is related to general distributed system (Dynamo, Spanner) but not quite the same). I also heard system research values industry experience more but not sure this is true (internship is from a big company but not in Tech industry)
Cons: is not research experience



To make thing complicated, I have contacted the professor before I got the internship offer and I don't know if I should talk my situation with the Professor. In addition, I'm an international student and if I couldn't get to a good PhD program, I may want to go to industry directly but I'm not sure if an experience in a research lab helps.

Questions:


Which one should I choose? 
Should I talk to the professor about my situation?
Does systems research value industry experience (more than other fields)?


PS: Thanks for the editing the format and input from comments
The answer depends on the people involved. If I were your professor, I would appreciate it if you would explain the situation and ask for advice. 

Of course, I would not give you any advice ;-), but I would ask you some questions which might help you finding a good decision - and maybe this is a hidden job interview.