1.) His skills with a katana are EXTREMELY good. At the level where he could actually keep up with Crono during Frenzy and possibly defend himself from a few of those strikes, possibly them all!
2.) There's a reason he looks like a douche. Because he is one. But by god, his determination, personality, and hilarity can make you want to be douchey like him half the time! Even if his goal is to be an awesome killer, you still feel like "Yeah! Go Travis! I wanna be the #1 killer ever!" And then someone you know walks in and hears that. (I was having a party and someone walked in on me screaming in a joyful tone "Woo! yeah! Die mothaf***a! I'm gonna kill them all!" I wound up having to explain myself to a couple of policemen later that night. I got them to wind up saying stuff along the same lines. And one part in 2 is a lie, though I think it's dead obvious which part it was.
Also to add, since his katana is charged by lightning, half of crono's attacks would only make him stronger as well so, I think although he's a parody character, he'd prove a formidable opponent.