MBA vs Engineering Mangament

I’m about to graduate with a double major in electrical and computer engineering. I’ve had a job lined up for months now at a fortune 50 company that will pay for a masters degree. What factors should I take into consideration when picking a masters degree? Does school matter? My current university is unranked and in close proximity to my future job so I was thinking of doing it there again. Will this hurt me having a bachelors & masters from an unranked school? My goal would be to move into management mostly likely as an engineering manager. I was thinking of doing a M.S. in Engineering Management or a MBA. MBA vs Engineering Management any thoughts here would be appreciated. Should I take a break before starting school again? I have 3 years of continuous engineering internship experience if that makes a difference. Thanks!

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