MORE GRIP 345 35 19 or 305 35 18

Note:Mistake in the title it's a 345 30 19

Well guys this obviously isn't for my stang. I posted elsewhere in another forum but I don't seem to be getting too much help so I was hoping someone here may have some experience. Long story short. Just brought my corvette (520rwhp 500tq NA, 625hp NOS stg1 900+hp NOS stg 2) out to palm springs. Mustang will be shipped here soon tooIt's the desert out here and the roads are perfect. It's the strangest thing though, the car doesn't hook. I did WAAYYYY better in chicago. I have kumho 275 40 18 MX's on it. In chicago it would grip pretty well, no NOS, grippedeverywhere but high rpm first gear. Out here the car is almost useless. Locals said it's because it doesn't rain and the road doesn't get cleaned. So here I am.

I'm looking at michelin pilot sport 345/30/19 or a Nitto Road Race NT555RII in 305 35 18. I know wider isn't always better and that's why I'm wondering. The NT is much softer compound. The cost diff is enormous as well. They both require a new rim but with the 345 I also have to do new quarter panels and paint. Which one do you guys think will be the better choice, strictly from a grip standpoint (not taking looks into consideration)