According to me Since the Power rating of devices are same and as far as conduction loss is concern Conduction losses occur when the device is in full conduction which further depends upon the energy dissipated in each transition multiplied by the frequency of operation of device.
Since switching frequency for Power diode is more than MOSFET and IGBT, Hence the later have better efficency.
What is the operating voltage?? If voltages up to a couple of hundred volts, you can find MOSFETs with very low Rds,on.... Up to 1.7 kV, you can find quite good IGBTs (MOSFETs are not feasible above 800-900V because of very high Rds,on) .... For voltages aove about 3 kV, IGCTs are the best in terms of conduction loss (IEGTs are comparable).. they however, come with their own requirements of di/dt limiters because of their Thyristor structure ...
The question presupposes that there is no variation within these types. You can rule out the IGBTs and Diodes for relatively low currents since they will maintain a higher voltage drop under conduction and the MOSFET transistors all have lower voltage drops in this range. Among the transistors, there is variation in Rds(on) for the MOSFETs and this only applies if you bias them correctly for full on use. Secondarily, you must be certain of the drive circuitry for rapid switching between on and off states since time spent transitioning between the two will represent power loss periods as they move through saturation and cutoff modes. The simple answer though is that the MOSFETs will dissipate the least power when fully on, up to 100s of amps, at least. IMO. This is, I repeat, an over simplification since one needs to know the voltages, currents and switching characteristics to make a good choice.
Although we have used IGBT for high voltage application, recently high voltage Silicon Carbide (SiC) MOSFET switches have been emerged which are very fast and have very low Rds-on. I believe that those king of MOSFETs have the lower conduction loss.
You simply cannot answer this question with the information given. There are many other contributing factors such as, current, voltage, frequency of switching and lastly, but perhaps more importantly, circuit application. An example would be, assuming DC operation, at lower currents, MOSFETs may prevail, while at high currents, IGBTs may be a better choice. Also, there are a couple of other device types that you should consider; SiC and GaN FETs to name just a couple.
You have to analyse conduction and switching losses for each type of device. The switching frequency will be a major factor. Semikron, Ixsys and TI have tools on their web sites which can be used to estimate losses and the most suitable devices for the particular circuit configuration.
If you are practicing as an engineer you need to use the web and read books on power electronics to bring you up to speed. If you are not an engineer you need to access engineering groups to provide you with advice.