Pros/Cons of using a Power MOSFET vs. a standard MOSFET
You should not only consider the requirements for the output section (source and drain). The gate section behaves as a non-linear capacitive load. A power mosfet requires the application of a high peak gate current and a reasonable gate voltage value (remember that is not suffice to reach Vth). Frequently someone says that the advantage of a mosfet over a bipolar transistor is that the former is driven by voltage and not current.  But this is a very incomplete statement, in the case of power mosfets. Depending on the application it's necessary that the gate driver circuit provides several amperes in a short time. In addition, other capacitances are present in a power mosfet that you must deal with. In other hand,  there are also standard mosfets with low values for RDSon. Therefore not justify the use of a power MOSFET in standard applications just for this reason, for example.