The anthology box CD set has been compressed. You can read about this on line. I have the compressed CD's AND the bluray of the anthology which is uncompressed (as the band hears it).
I am afraid you prefer the sound of compressed music rather than the more open natural sound.(many do and that is why they master CDs hot - see loudness wars on google). On a system that is unable to play loud then the compressed music will have more punch and sound good at lower volumes. On a setup that can play very loud you will really get the live sound of the band with the uncompressed sound (from bluray or 24/96 HD with Tom Petty as Ryan has already confirmed that the CD's are compressed for regular consumers)
I know this will probably be controversial because everyone here thinks that they would prefer less distortion and not more, however, google the Ryan Ulyate interviews and it will confirm what I am saying,