Relevant characteristics are Rdson versus Vgs, and Rdson versus temperature.
Usually, power transistors are used in the linear regime, i.e. at low Vds (so that Ids is proportional to Vds).
But in some applications, power devices operate at large Vds (and low Vgs) - in which case, characterizing Rdson dependence on Vds also makes sense.
Also important is Ids vs Vgs at various temperatures - it will show a "temperature compensated point" = a value of Vgs below which Ids increases with temperature increase (due to lowering Vt), and above which Ids is decreasing with temperature (due to a decrease in carrier mobility). Operation at Vgs below a temperature compensated point may be unstable with respect to temperature.
All the things mentioned above are related to DC operating conditions.
For transient operation, gate charge curves, capacitances - Cgs, Cgd, Cds - and their voltage dependencies, switching times, reverse recovery times, etc. are important.
You can look at any datasheet of a discrete power transistor, to see what characteristics are important.
Also, do not forget about various parasitics, always present in real designs/layouts, such as resistances of metallization, wirebonding, etc.