Bassamatic brings up some excellent points.
Since you guys seem to be okay with the POW example, I'm going to take this idea a step further as it relates to limiting. Remember what I said earlier: In the world of compression, volume is a relative thing. With this in mind, I'm going to throw something out there that is really important:
POW is the same as pow.

Right? Think about it. Think of a really busy magazine advertisement. If you emphasize everything, then you emphasize nothing. And if you make everything louder, then you're really just sucking the life out of everything in equal proportions. The reason I bring this up is because some mastering engineers in the 90's and 00's started this trend that, sadly, hasn't let up much ... of just trying to squash everything, thinking they were actually making a louder and more aggressive mix.
Anyway, enough of my rambling on that topic. My point is that it's just as easy to do it with a bass as it is with anything. So just don't do it.
On the subject of "PUNCHY"
What we've been talking about so far with attack and release times, and how they effect the word "POW!" ... we're essentially talking about an "envelope" (you'll hear that term used). And what the attack and release times do is set the envelope's shape. By setting a slow attack and moderate release, we create Pow. It's "envelope" would be a slope, descending from left to right. Now if you were to do the opposite and use a super-fast attack paired with super-fast release, it would look like pOW, so the shape would again be a slope, but in the reverse direction.
Now if you get your attack and release settings just right (and it does take some fiddling) ... you can even get a "v" shape like this: PoW, or even a tent-shape in reverse like pOw.
Tent-shaped pOw: would be basically all fundamental, and no definition. Think more of a "jazz" bass tone. Amost "gated"; sometimes even mushy.
V-shaped PoW: Very defined. Very forward. Very in-your-face. When mixing a record, I (and others like me) like to use this envelope shape for vocals, because it will place the track front and center. This is especially true for voice-overs and radio, where annunciation is much more important than tone. But the same principles hold true for all instruments and tracks. By emphasizing the beginnings and endings of words (or any audio event), you make it more defined, at the expense, sometimes of de-emphasizing the actual "tone." When you think of the V-shape, think "hi-fi," and when you think of the tend-shape, think "vintage."
Reverse-sloped (ascending) ppoOWW (added some extra letters to show it in slow-motion). This is punchy boys and girls.. If you want more clarity with the punch, you can slow the attack time to get more of a U-shaped (or smiley-face) PpoOW.
Look at that for a second: PpoOW!. It even looks punchy. Like an actual, physical punch, it kind of cocks back (with the small p and the o), and then it accelerates before sssmmmACKING! you in the face. Let's look at that again in slow motion. ssssmmmMAACK!! Ouch.
Why does this shape work so well for bass?
Think of what you're doing with your fat finger when you pluck a string. In a sense, you are putting tension on the string and "cocking" it back like you would a sling shot or a water-balloon launcher. The sound is created when the string is released and "snaps back" in to position and then resonates. With the compressor, the reverse-slope (or even the v shape) envelope accentuates this action by emphasizing this "snapping back." And that's where the punch is.
So, in short, punchiness is all in the release time, interacting with your fingers (or pick). If you can time out the release to create an envelope that sssmMACKS! you with that exclamation point at the end, then you have a track oozing with punch. Now if you can actually get to the point where you can time that release with the beat of the music (very very hard to do by the way so don't sweat it too much) ... then you put that in the pocket with the kick drum, so that the kick and bass both deliver that shape as almost one instrument ... then you create a sensation that moves people. If it's funky, then listeners will want to dance. If it's aggressive music, then it will start a mosh pit. If it's smooth and romantic, then couples will be making sweet love to your uber-punchy bass line.
Now that I've just given my trade secret for punchy bass away, I hope that you will use it to move people to do good deeds for fellow mankind.