Also, a big thing when it comes to compression vs valves/overdrive is attack/release time.
A compressor has an adjustable delay before it clamps down on your signal. This means that your signal isn't just evened out, the initial peak can in fact be louder and more pronounced than it was before. With a multi band comp, you can apply this trick to the lows so that every note has a 'pop' to it, but have a faster attack time akin to a limiter to control the higher frequencies associated with aggressive playing.
Your valves won't do this, but a Spectracomp will!