This question is not one sided. My answer is that you should do both-- however, I would suggest getting the PE first, then the MS. Why? Graduate school is most beneficial and valuable when you have 4-7 years of real work experience under your belt. You understand the concepts that they are teaching, have probably been introduced into some of them and have a much greater grasp of the "big Picture." Folks who go directly from a BS to a MS really cheat themselves-- they don't have the experience to be able to really argue and make great points in a controversial discussion. Not a knock on them, they just don't have the experience.
You can get your PE 4 years after your BS. Anyone with a BS should be working on his/her PE as soon as they graduate. Those 4 years come and go FAST! Get your PE and then go to graduate school. Many companies will pay for a graduate degree-- in fact, most good universities will offer scholarships for American students in graduate school. If you check out most good graduate programs, almost 95% of the students are foreign students. Why? American students are making money in their profession. The foreign students want/need the graduate degree either to stay here or go back to their home country. Most after being in America, desire to stay here and hope to get visa sponsorship with their graduate degree.
The NCEES B+30 rule which will be enacted in 2020 strongly suggests getting a graduate degree-- in fact, most masters degrees are about 36 hours beyond a BS. Now, many states have NOT and I suspect, will not, agree/concur with NCEES and require the +30 hours for the PE license. However, you can see that sooner or later, it will happen. There is precedent-- in order to become a CPA, you have to have 150 total credit hours to sit for the exam. Some folks just take another 30 hours in subjects which they enjoy. However many folks go on and get a Master's degree in Accounting, which fulfills the +30 hour requirement.
It will only be a matter of time before engineers will be required to have the B+30 credit hour rule. It may be 2030 before it happens, but it will happen.
OK, my take--- get the PE ASAP. As is cited above, you need continuing education hours, but you have the PE. AFTER you have the PE in hand, then go for graduate school. Get into the BEST graduate school you can---- the best ones even have online delivery modalities which work.
The MBA-- the real truth to the question is that if your MBA is not from one of the top 10 MBA programs, it really is not as valuable as the admissions folks told you it was. Granted, you will learn a lot of great material and will be able to use it in your job, however, the top 10 MBA programs are the ones that really command the real dollars.
Don't worry about dollars. Dollars come-- maybe not as fast as you want, but they do come along. Get the PE then the MS. You will be golden at the end of the road.