Choosing between Bachelors's in a higher uni vs masters in less reputable uni? I graduated with an EE degree last year and interned in two Physics labs, From September until March for experimental physics in Lab until COVID struck and lab closed and another one from Mid Summer (June) until September in computational physics (still continuing part-time I will come to that later).
Been applying for the Fall 2021 cycle to Physics Grad programs however I was told that I lacked a Physics Background [ Had only taken EM classes and maybe 1st-year basic waves and mechanics].
Recently I got in BSC honors in Physics in a reputable university [will take roughly 2 to 2.5 years] along with another offer in Masters in a less reputable university with a requirement to complete a qualifying year (consists of higher Physics undergraduate courses). I talked with the department and supervisor who has told me that funding is available for research as well as some money from being a TA. I was only able to get in due to a connection from another prof in another University who very much vouched but failed to convince the admission committee in his University (due to lack of physics background). So I would also assume that the supervisor has done the same.
Being torn I don't know what I should choose, I feel l should choose Bachelors and then apply directly for Ph.D. while masters and then Ph.D. would take the same amount of time. In  addition, my current research professor is very enthusiastic about what I have done with the detector simulation software development (he is the leader of the research group I am in which I can't specify for personal identification reasons) and he has suggested a collaboration with the university which I want to do bachelors in and wants me in future after I complete bachelors.
Financially speaking I would assume that Masters would be slightly less expensive than doing Bachelors (from approximate calculations I have done).
I am just very much torn between these options, the professors on both sides have gone out of their way to help me pursue my passion.
Additional follow up: Does it matter where you do your masters for Ph.D. (plan on pursuing an academic career)  in terms of university ranking and reputation?
Sorry for long text, and thanks for any advice, suggestions!
Paying for a masters degree in physics is a poor idea, even a poorer idea is a second BS in physics.
Get an engineering degree if you're going to spend your own money.