with everything similar, car, engine, suspension and wheel...
will the car get more traction with:

275/40/17 on 17x10 wheels
or
265/35/18 on 18x9.5 wheels

 

Simple answer, 275/40-17 Hoosiers on 10 x 17 wheels.

Reason--you have more rim width and tire width with the 275-on-10 versus 265-on-9.5.

Although the 265/35-18 is the same overall height as the 275/40-17 Hoosier, the Hooser has a slightly taller sidewall which contributes to better breakaway characteristics than shorter sidewalled tires in the same compound

I presume you're using Michelin Pilot Sport Cup Comp or Ecsta V700 in the 265/35-18, since Hooser doesn't make that size. They make a 275/35-18 though.

Nonetheless, the Hoosier is a superior track tire to Michelin (certainly better than Kumho) with regard to ultimate tire grip and handling. Of course Hoosier R3S03s are the lightest tires out there, and Michelins weigh more.

Can't argue with Hoosier Racing Tire Sports Car DOT radials. That's all they make. And they're damned good at it! www.hoosiertire.com

FWIW, Porsche Panorama did a tire test comparing the P-Zero Corsa, Ecsta V700, and Michelin Pilot Sport Cup Comps, using a late-model Porsche 996 Carrera in tire size 225/40-18 front and 265/35-18 rear.

The results were: Pilot Sports > P-Zero Corsas > Ecsta V700s.

Won't get into the details, since it's off-topic, but there was real tire temp and laptime data.

 

what if the tires were same brand, which will have more traction?

I personally loved the set up with hoosier 275 on 17x10...

 

...depends on what kind of driving you're doing. Generally, the wider, with slightly taller sidewalled tire will have more grip, and more predictable breakaway behavior.

Quote:

I personally loved the set up with hoosier 275 on 17x10...

...had that setup in back except with 9.5 wide. The 275/40-17 Hoosier really needs a 10 wide rim to make 'em smile (as bradrx7 would say). I'd love to be able to run four 10 x 17 with 275/40-17 Hoosiers all around.