The benefit of a grad degree is an easy question, but the answer can be quite involved. This could easily be a topic for another discussion.
I assume that you are looking at a job in industry as your end game.
There are many different types of engineering jobs in many different industries, so a general answer that fits all is impossible.
I worked in the aerospace world, specifically on NASA projects. I worked most of my career for one of the BIG aerospace companies but did some long-term consulting for a small (25 person) company. So, my perspective is somewhat limited.
Using my experience as an example:
As I approached the completion of my BS I wanted out of college. I didn’t know what, other than engineering for NASA, I wanted to do. It seemed like starting to get more specialized within a master’s degree program wasn’t the best thing to do. I was offered a job within big aerospace doing analytical work. I wasn’t sure that is what I wanted to do, but it was my only offer. So, I took it. After about a year at work I swapped jobs with another guy and worked in design for about 6 months. When it was time to switch back (I was offered a permanent position in design, if I wanted it), I knew the analysis area was where I wanted my career to go. I also knew that an advanced degree was in my future. I eventually went to grad school in a applied mechanics / applied mathematics department. Something I would have never considered if I had gone straight to grad school from my BS.
So, my advice. Let your interests dictate what area of engineering you go into. If at the end of your undergraduate degree, you know what area you would like for a MS degree, then go for it. Otherwise, you can always work a while and see where your career takes you and whether an advanced degree is warranted.
I ended up in management. The size of my group varied a lot. We worked on some pretty cutting-edge NASA projects. At one point I had about 25 engineers reporting to me; 8 had their PhD, 14 MS and only 3 BS degrees. Many were like me and started work with only their BS. Some took leaves of absence to go full time to grad school while others worked and went to school part time. I did the part time thing and it is a long process. But marriage and kids dictated it be that way. As I was learning new skills in the MS program, I was able to apply them to my job and so my performance at work got better even though hadn’t yet completed my degree.
Other than my group, most of the other engineering functions were dominated by holders of BS degrees. So, it does really matter what is the end game of your career.
The other thing to consider, is that no matter what degree you have, it is your performance on the job that matters most.
One last point, companies (like mine did) will pay your tuition for an advanced degree. Funding is always a question going for the degree right after your BS.