Engineering Masters should I continue in engineering and then do MBA or switch to consulting now?

I am a masters of engineering student at U of Toronto. I did my undergrad in engineering for the same school and worked in manufacturing and R&D for a startup electric automotive OEM that ultimately failed. I will be finishing my masters mid next year and would appreciate feedback on what my options are.

I have currently caught the consulting bug not because of the pay package or the travel but because I really want to work on big picture business problems rather than engineering solutions where I believe my impact is rather limited. My undergrad GPA was bad but still was able to achieve a thesis based masters admission based on my work experience and very strong extra curriculars. My current masters GPA is 3.7. Would getting into an engineering firm and then pursing MBA be a better option to then switch into consulting? Or will getting in as a analysts at one of the consulting firms and then doing an MBA to switch to a Associate/ consultant role be a better option? Would MBA schools prefer one path over the other?