ALO RX, Headstage Arrow, RSA amp VS comparable home amp.

This may be a no-brainer, but I just wanted to put it out there. Is there a huge difference in sound quality between on of the portable mid-high grade amps and their similarly priced, desk sitting and wall leaching counterparts such as the Matrix M-Stage, Schiit Asgard, or even an old headroom amp from 1999 that is on sale now? I'm talking about hearing the music jump out from the amp from even low volumes, and have impact and realism. I currently do not own any amps, just a cheap CD player that puts out a lot of power but lacks clarity and hisses horribly from its headphone jack. Thanks to everybody who helps me out on this.

Side Note: No, I am not forseeing buying the items in my picture anytime soon.