Agree with that ^^^^^^^^^
I dabble with surf and psychobilly music for fun, but my main gig is hard fast punk rock and I play through roaring Marshall stacks set to kill, so my experiences probably fall outside of the typical 60 Custom user. But I feel I have a pretty good handle on my own 60 Custom anyway. I can't speak for the Swept Wing, but the 60 Custom handles it all very well. Beautiful build, fit, and finish that rivals and/or exceeds any custom shop stuff from Gibson or Fender. I bring my Les Pauls and SGs to gigs, the Hallmark 60 Custom is the only guitar anyone even looks at. It's functional art. But more importantly, it's a player and plays great to me. It can handle my ham-fisted abuse just fine. The neck is similar to a semi-flattened 60s Gibson neck. It's not the narrowed micro Mosrite neck, and to me, that's a point in Hallmark's favor. It's a physically big and somewhat heavy guitar, but again, to me that's a good thing.
I think the 60C will generally sound much fatter than any Strat or Tele though. If you're looking for that piercing bright kind of twang, that's not the 60 Custom's forte. It's stock pickups are fat and thick and sound pretty great for the plonky Mosrite sound. If you need a tighter, brighter bridge pickup, ask for the Fat Pig.

Or go with 500k pots as mentioned.
Not to spam myself, but here's a clip of my 60 Custom in action through some very un-surf-like Marshalls. It sounds great through any amp.
https://dl.dropboxusercontent.com/u/262 ... nsters.mp3P.S. - Bob Shade is a cool dude and a pleasure to do business with.