EQ will level out, cut, or boost certain tones (bass, mids, treble, some in between). I've never used compression before.
compression will even out your dynamic range. it makes you loudest sounds a little less loud and will increase sustain if you use it right.
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whats a good compression for like hardcore music like .the devil wears prada, as i lay dying,underoath kind of music?
Well if you're using distortion it might not matter too much. Distortion kind of already has a natural compression. You'll notice that with distortion there isn't much volume difference when you play harder or softer. Especially if you are using a lot of distortion. Compression would be used if you notice that the volume level of your playing is uneven. It's almost always used for vocals for instance, because even the best singers have volume shifts when they're singing higher and lower notes.
You don't use compression for "hardcore music"....

you use it for cleans... think john frusciante, red hot chili peppers... he uses compression quite a bit.
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They'll do nothing if you're running direct into a PA.

An EQ pedal is an expanded, more precise version of the tone controls on an amp, it gives you control over specific frequencies rather than the very broad sweep of a normal bass, mid or treble knob. They're also active, meaning they can boost frequencies as well as cut them making them much more useful and a powerful ton-shaping tool. Arguably an EQ pedal is more useful than a distortion pedal if you have an amp that doesn't quite have the sound you want.

Compression won't do much of anything for you, I doubt you'd notice it anyway as it's a relatively subtle effect. Really useful for cleans as it allows you to play with the attack of the notes and get some more sustain, lots of country players use compressors.

Not so useful with distorted tones, and generally the more distorted you get the less you'll find a use for a compressor as they tend to make things quite noisy. You've got little need for the sustaining qualities a compressor can add because you get that anyway from turning an amp up and adding gain.
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You could use compression for hardcore or actually any music.

a comp pedal is no different then the compression they do in the editing of those guitar tracks you hear in songs.

A great example of compression used all the time is "Billy Talent" you can check them out at http://billytalent.com/sections/listen/player.html

listen to "Pins And Needles" & "Try Honesty" both compression... just different rates of it.
Get a Keeley Compression Pedal.
Or an MXR, anything thats NOT made in China.

China = crap
Japan/mexican/usa = pro