First, you should use a comparator if you want to do comparisons.
Choose one with a switching time substantially less than what you want the overall switching time of the circuit to be (with 1 ms spec, you should be able to choose almost any of them).
Second, choose one that can drive enough output current to pull the FET gate full swing quickly enough. On chat, you mentioned the DMG9M65CT, whose datasheet gives a gate capacitance of 2.3 nF. To switch this by 5 V in 1 ms requires about 10 uA of current. Again, you should have no problems finding a comparator that can do this. (Your problem would be harder if you wanted to switch in less than a microsecond, for example).
Third, choose whichever comparator has the lowest price, is available for immediate delivery, has the package you want, comes from a vendor you trust, etc.
Final note, remember that many comparators have open drain outputs. That means they can only pull their output low. You'll need to have a pull-up resistor to pull the output high when it should be high. Choose the highest-value pull-up resistor that gives an adequately fast switching time for the low-high transitions. With a 15 V positive supply available, this could be as high as 50 kohms, but if your available supply is not very much above 5 V, you might need a much lower value.
Best Answer
In general, an analog comparator could be defined as any device intended to compare two analog quantities using analog circuit techniques. In most practical cases, the two analog quantities are voltages and the most common circuit technique is a voltage comparator. However, for example, you might need to compare two resistors for which a Wheatstone Bridge would be a suitable analog comparator device. Thus, a voltage comparator is an example of an analog comparator but not all analog comparators are voltage comparators.