RV-12 Flight Instructor reported on departure experiencing a rough running engine with power drop resulting in the return to the departure airport where they landed safely.

Narrative

Conducted a typical training flight with a new student on Day 0 at XA:15pm local time. This was the students third flight.Engine runup and performance was normal and without incident. Departed Runway XX at ZZZ. Winds were 160 at 8 knots. The student was at the controls during the initial climbout when at approximately 400 feet AGL the engine started running very rough and engine power dropped from ~5000 RPM to ~3900 RPM. Along with engine roughness there was an oil burning smell coming into the cockpit. When this happened; I took the controls and immediately started turning back towards the airport and circled to runway XX.Prior to circling to runway XX; I initially planned on returning to runway XY but mismanaged my airspeed (too fast) and would not be able to safely land on XY. Since I still had engine power I continued around and landed on XX. As I've been replaying the situation; I'm questioning whether I should have continued flying the pattern or if turning back towards XY was the best course of action.Another factor in my decision to circle to XX was a second aircraft had lined up and was waiting at the departure end of runway XX. I did not hear any radio calls from them and was concerned they would start their takeoff roll while I was attempting to land the opposite direction on XY. That aircraft exited the runway while I was approximately midfield downwind to XX.Ultimately we were able to land safely and without further incident.