Current MS3 and former paramedic here. I'm not on any admissions committees so I can't speak with much authority to that, but I don't think most adcom members understand or care very much about the distinction between an EMT and a paramedic unless they worked in EMS themselves.
Obviously, a paramedic has a lot more education than an EMT, and that might offer a slight advantage once you've matriculated. This is especially true for skills like interpreting EKGs and procedural skills (e.g., starting IVs, intubating). However, these make up a pretty small segment of medical education, so I think there's limited value there. Additionally, a lot of the operational skills that EMTs and paramedics learn (e.g., drawing up meds, attaching monitors) are simply not necessary for a physician, since in the hospital, these tasks are much more commonly performed by nurses and techs.
In a traditional EMS model, paramedics have much more of a leadership role than EMTs during a patient encounter. That might mean directing other people, determining when to escalate/de-escalate responses, making judgment calls on differential diagnoses and treatment plans, and taking final responsibility for decisions. Since physicians are generally expected to take on a similar degree of responsibility, being a paramedic might better prepare an applicant for adopting the "physician mindset."
I do not think that most medical students are expected to take this level of responsibility or leadership, so the added value of being a paramedic (vs. an EMT) is certainly not necessary, but it can definitely set someone apart. It could also potentially be a positive if viewed by an adcom member who places a higher-than-average value on leadership.
Speaking for myself, I was a non-traditional applicant with a pretty bad undergrad GPA, so I leaned really heavily into my leadership experiences. I don't think this would have had as much benefit for a more traditional applicant, but I used it to my advantage.
To sum it up, upgrading from EMT to paramedic can offer value in a few niche circumstances, but probably isn't worth the extra 1–2 years of schooling for most prospective medical students. However, if the student falls into one of those niche circumstances, there can be considerable value.
