I'm guessing Steve is not a very aggressive rider, I've ridden all the Kawasaki triples "back in the day", and they weren't called "Widow Makers" for nothing. Do a google search and you'll find tons of information on how to modify them to make them handle as well as other bikes from the era.
That doesn't make them bad bikes, they were wickedly fast and light, and until the mighty Z1 came along, the H2 was the fastest bike on the planet and would leave a CB750 or Suzuki GT750 in it's dust. When I was a kid one of my local heroes had a black H2 with 3 separate chrome expansion chambers, and he'd see me and wheelie past my place at warp speed, that bike was a weapon!
The Suzuki triples were great, torquey 2 strokes with a wide power band, but heavier than the Kawasaki's, especially the GT750 (my fave) due to the extra weight of it's water cooling. The Yamaha RD 350 (air cooled) was a great bike, I still remember sitting on the back of a mate's R5 (RD350's predecessor) @ 105 MPH with the cop car's flashing lights fading in the mirrors, they were quick.
The later water cooled RD/LC's were better again, and the final RZ's (including the very rare and expensive RZ500) were spectacular, as was Suzuki's last 2 strokes, the RG250/500 (unobtainium) and RGV250. Aprilia liked the RGV so much they used the engine in their sexy RS250. Cheers, Terry.