Both matter but in reality, there are a million more variables than just tires that'll inspire confidence! Suspension and chassis geometry are also just as important.
A great rider can ride a bike that most of us would think has the crappiest set of rubber and actually suprise the hell outta you. It's all about knowing the limits of traction available, using the slide to your advantages and controlling it in a manner that helps you improve your entry, apicies, and exit speeds.
but....
a good tire is VERY CONFIDENCE INSPIRING and help you to improve your skill. An example for me was yesterday at Willow Springs Big Track, I used the trackday/street hybrid BT002RS and found some major confidence in my turn-in ability, cornerspeed, etc. Previously, I used a set of Bridgestone racing slicks that had a slightly different geometry compared to the 002RS and I had ZERO confidence in my cornering ability. That is due to the way the tire changed my overall chassis geometry and gave it a different handling characteristic. My suggestion for you is to try: Dunlop Qualifiers, Michelin Pilot Powers or 2CT's, Brigestone BT002RS, Pirelli Corsas, or any other tire of an equivalent mentioned above. You will see your confidence shoot up dramatically.
HOWEVER, WITH THAT SAID, WORK ON YOUR SUSPENSION FIRST. You'll actually gain more than just swapping tires. Tires and suspension go hand in hand. If you're a heavier rider (>140 lbs), swap out them stock fork springs and go heavier. Adjust your preload to proper SAG measurements (for better twisties riding, go closer to race sag than Street, but not full on stiff like race sag), and dial in your compression/rebound settings. you wanna dial in comp/reb to when you compress and release the front end or shock, the bike should compress, but return to it's static height within one second. That's general rule of thumb.
