This is an interesting question and would be a great bit of doctoral research. I think it would be good to cover a large number of people just to increase the strength of the data.
We'd have to have three groups, commuters, recreational riders, and drivers/public transit riders (control). Each commuter would have a corresponding rec rider who would ride the same route as the commuter, but NOT on a day they were working. The study would probably be done only 2 - 3 days per week, since the rec riders may only have the ability to take the route on weekends. Consequently, to accurately measure the physiological impact, the commuter would have to reduce their commute to the same number of days as the rec riders. A small study of about 50 per cohort would provide enough data to give it some weight.
Cortisol levels, BP, pulse, could be measured before and after ever ride for every person. Qualitative data could be collected by having all of the participants each answer a standardized survey after their particular activity.
It's a great question to ask and when measured against the control, it could provide more ammunition for bicycle advocacy.
Personally, I prefer commuting to work on a bike because it prepares me for the day (I'm a mental health therapist in one of the larger medical centers in Philly) and helps me to leave it behind when I'm done. This past week was incredibly busy and with the remnants of a tropical storm over us for 4 days, I made the 10-mile commute to work in the car because of parts of my route being flooded or at risk of flooding, and awful Philly drivers whose technique doesn't improve in the rain.
Yesterday, finally got to ride to work and I didn't feel exhausted like the previous days in the week. I felt energized and much more mentally prepared for my job in spite of not getting enough sleep during the prior days, and feeling like I was dragging myself around with only willpower, not real energy.