Obviously the benefits or comparison of private vs academic vary by the person and the specific situation, but I will try to explain what the tradeoffs are from my perspective and how I made my decision.
Private:
Pros- pay is generally higher, probably in the range of 20% higher, with a higher ceiling depending on how busy you are. Less oversight and management from above, more autonomy. No responsibility to teach medical students or residents. No mandatory committee meetings or yearly evaluations.
Cons- Most are guaranteed salary only for 1-2 years, then its eat what you kill. So constant pressure to be busy and productive and no guarantee that your salary remains high. Depending on the practice, you may be responsible for day to day operations, overhead, hiring and firing, marketing yourself, building relationships. May need to cover multiple hospitals. Call responsibility is usually more frequent and onerous. May not have the OPPORTUNITY to teach medical students, if this is of interest to you, but more importantly, may not have resident coverage for overnight floor calls, ED consults, etc.
Academic:
Basically the reverse of above.
I am an academic surgeon, because I valued the ability to teach students and residents and the stability and "guarantee" of the academic environment, as well as the infrastructure for research and innovation, more than the 20% salary bump. Other factors that went into my decision are things like the relative ease of going from academic to private compared to the going from private to academic, i.e. if I decided after 5 years that I hated academic, it is easier to transition to a private job, compared to the reverse. This may be incorrect thinking on my part as I dont have first-hand knowledge of the ease of either transition but it seemed likely to me at the time.