What would you say is a faster a shallower rim with a tyre size that matches the width or a narrower but deep section rim with a tyre that’s wider than the rim?
There’s a million other factors (and options) that have to be taken into consideration. Tire size? Course? Climbing? Terrain? Wind? Weight of each option?
I would say that given only the two options, narrow and deep would be faster on a road bike with a narrow tires and not a ton of cross wind. If there’s a ton of climbing, maybe wide and shallow if it also means lighter.
Do you have an option only between the two, or can you provide more context on the other info I mentioned above?
@davidsparkinson it depends! 
What’s the wind like? The more crosswind you have the more you have to favor obeying the Rule of 105. What’s the surface like? The more the surface is rough the more you have to favor wider tires. What’s the rim profile difference? All things considered, the aerodynamic advantage of, say, a 50mm deep rim vs an old-fashioned box rim is hard to beat regardless of tire selection. What’s the rim cross section look like? A v-section deep rim with an ice-cream-cone tire on it is decidedly dodgy in the wind…and the tweakiness of that sort of setup can sneak up on you…riding down a hill with the sun in your face you may find that swirling winds (thermals) will give you white knuckles…or head-on passing a tractor-trailer on a 2-lane road may feel like the handlebars are jerked out of your grip.
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Basically I had a set of profile 50mm front 80mm rear. I’ve worn the brake track out so need new wheels. I can’t be bothered with carbon rim braking and deep section anymore to be honest due to cross winds. So I’ve gone for some 30mm aluminium wheels and these happen to be a little wider. Was just wondering if the width makes much difference.
@davidsparkinson I have a bike w/38mm deep alloy rims, 30mm tires, 23mm rim width. I’ve never been able to measure a difference between that setup & a setup with 25mm tires & same rims. There may be a difference, of course, but it’s not big enough to measure. I guess the aerodynamic disadvantage of the wider tire is almost exactly offset by the rolling resistance advantage.
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@brennus that’s the impression I get from real world experience, you can’t really tell the difference. I’m current using some 40mm vision carbon wheels and I can’t tell any difference between them and my old 50/80mm profile wheels. I might be getting cynical I my old age but I think the industry is just trying to sell us something.
Maybe some super fancy wheels will save me 30 seconds in a 40k triathlon bike leg but when I’m losing minutes in the swim and run who cares 