Answer: Well not a lot besides technique. At least not in the manner that you phrased your question. The reason you're getting ringing sounds when you're sweeping is your own technique. It's not the guitar or the amp. Sweeping is an advanced technique and either something that you can pull off or you can't. Half-assed sweeping sounds terrible. Of course, I'm not trying to discourage you. Practice makes perfect. You must mute the strings that you aren't picking in order for a sweep to sound clean. Other than that, like I said, most of your 'sound' comes from you. There's no hiding behind gobs of distortion or effects that'll save one's playing. Besides having good technique, however, obviously your tone is effected by your amp (and how you actually set the EQs) and also your guitar. Different pickups will obviously produce different sounds.
But 'that sound' that you're referring to is manifested in your own playing ability.