How does a person know if they are making a high current, high watt amp, or not?The first thing to understand here is that power, current and voltage have a direct relationship; 1 watt = 1 Amp x 1 Volt That's called the Power formula, and like Ohm's Law, cannot be violated, unlike a speed limit :)
So right away, if you work the math, you can see that a 'high current' amplifier is a misnomer. You can read more about that here:
http://www.atma-sphere.com/Resources/Common_Amplifier_Myths.php
One thing about filter capacitance: the amp circuit has timing constants in it, usually a coupling capacitor somewhere, which rolls off at some low frequency that can be calculated. The power supply has timing constants too (it takes a certain amount of time to discharge the filter caps based on how much current can be drawn from them); for best results the power supply should always have a timing constant considerably lower than that of the amplifier, otherwise low frequency instability and/or intermodulations can result. You might be thinking 'what about amps that are direct-coupled input to output?' and its a good question. They will always have the ability to modulate their power supplies!
This is why you tend to see excessive amounts of filter capacitance in solid state amplifiers. Now its a pretty good bet that the amp won't see really low frequencies that will get it in trouble, due to the fact of timing constants rolling off in the sub-bass octaves upstream. But if there gets to be any noise or sag in the power supply, in a solid state amp that can be pretty audible as transistors tend to be more sensitive to voltage variations in the supply than tubes (generally speaking of course). So large filter banks are common in such amps.