Hey guys,It's been 6 months since I've started playing guitar again after quitting couple of years ago and recently been feeling that my guitar sound better when I listen through my headphone. 
( Ive got a Squire CV60 and a Orange 20RT, no mod or anything done.)
But to be exact, Its the clean tone that sounds how I wanted through headphone while the distortion/overdrive sounds always better through amp speakers. 

I'm a huge RHCP fan and trying to pursue John Frusciante's 2003 Slane live tone. So through headphone, the clean tone sort of sounds like JF's greasy clean but through amp speaker, It sounds very dry and doesn't resembles headphone's clean tone at all.   
 However, I've used to DJ and have a Sennheiser HD 25 which cost same as 20rt. So I was thinking that the quality of speakers/amp for HD25 were better compare to 20rt, thus causing huge tone difference? 

Because when I've first started playing guitar couple of years ago, I remember my guitar tone sound horrible through cheap headphone I had. 

So I was thinking If I replace the speaker in 20rt, It could give that tone I wanted? I really like my gears and have no plans to upgrade anything soon, so thought modding would be the perfect option for me. What do you guys think? 
The amp itself is probably what is holding you back the most. I would not bother modding it, look into getting a proper tube amp. See what Frusciante uses, get something that will get you similar results in a consumer budget.
What settings on the amp? Maybe something there could be improved.

I have noticed that with some small solid state amps that the phone and line out signal quality can be really quite excellent. The electronics can drive a high impedance load with a very low level signal easily (typical head phone load impedance only draws a few hundredths of a watt - like 0.025 watts - to produce full high volume listening level). Changing the speaker will likely make no difference because the new one's rated load will need to match the present load for the circuit.
Quote by reverb66
I'm pretty sure the Bible requires that you play through a tube amp in Texas.