By all means determine your cost constraints and finances and check out the net price calculator results for both schools. Rutgers, as all of New Jersey’s public colleges, is not particularly inexpensive. The majority of Stevens students receive merit and need based financial aid and find that they can attend for approximately the cost of attending a public university. Cost aside, from an academic and job placement standpoint Stevens is significantly stronger than Rutgers in engineering and physics in general. There is significant government and industry sponsored research taking place at Stevens in physics, particularly in the areas of quantum devices (a major research program is to develop room temperature quantum semiconductors, which will be a breakthrough in the field), communications, computation, and quantum information science. Undergraduates are involved in this research as well as graduate students and is really a unique opportunity.
If you go the engineering route, Rutgers has no ABET accredited engineering physics programs. They have an applied science program in the engineering school, but it is not ABET accredited as an engineering degree. Stevens has an ABET accredited engineering physics program specializing in optical engineering. There are also programs in nanotechnology, nanophotonics, and solid state physics which can be taken in the electrical, mechanical, and other engineering departments but can include a substantial engineering physics component.
https://www.stevens.edu/schaefer-school-engineering-science/departments/physics
I would recommend both Stevens and Rutgers over NJIT if you are interested in physics. NJIT’s physics department appears to be mostly a service department (giving the prerequisite foundational physics courses to engineering and science majors as opposed to high level research as is the case in the former two institutions). Their programs are advertised as applied physics, if you are interested more in theoretical physics Stevens or Rutgers have more in this area. Their physics offerings are in collaboration with Rutgers-Newark, which has more resources in the field and has a true standalone physics department.