In racing engines without valve diameter limitations, you fit the largest intake valve you can that won't shroud (excessively) or have clearance issues and the exhaust gets whatever is left.
On the intake stroke, you have ~14 psi in the intake filling a cylinder that's 3-4 psi lower (at most). On the exhaust side, there's 100+ psi residual combustion pressure in the cylinder when the exhaust valve opens. The engine's fart is screaming out of that cylinder in blowdown with the rest being pushed out by the piston or scavenged during overlap. Thus, you don't need as much valve curtain area on the exhaust side. The smaller exhaust valve also helps prevent reversion.
Another reason, more durability than power or efficiency, is the ability to open the exhaust valve against cylinder pressure. A 1.60" valve has a surface square area of 2.01 in^2. With 100 psi residual combustion pressure in the cylinder, that's 201 lbs holding the exhaust valve shut. The valvetrain must overcome that just to get the valve to crack off the seat. Then the spring seat pressure is added to that and multiplied across the rocker ratio (if such valvetrain configuration has one). Say spring seat pressure is 200 lbs, that's 400 lbs at the valve/rocker tip, and across a 1.5 rocker ratio would be 600 lbs at the pushrod and lifter. (on a center cam V engine) A 2.05" valve (common small block V8 intake size) has a surface square area of 3.3 in^2. Against 100 psi cylinder pressure, that's 330 lbs + 200 lb spring and then x 1.5 rocker = 795 lbs at the lifter. Even direct cam on tappet will see a tremendous difference. So having a smaller diameter exhaust valve is beneficial in reducing stress and shock on the valvetrain, thus also reducing torsional vibration, and increasing longevity/durability.
EDIT: To add a side bit of information... NHRA Top Fuel engines, making 11,000 HP with ~70 psi boost in a 500ci engine on nitromethane, are actually hindered significantly at that power level because of the exhaust valve and cylinder pressure. They have to open the exhaust valve way later than they'd ideally want to due to the extremely high cylinder pressure. They're opening it at ~75° BBDC when they'd ideally want to be closer to 90° BBDC. If they tried to open the exhaust valve at 90° BBDC, the cylinder pressure is still >1200 psi at that point. With a 1.925" exhaust valve with 2.91 in^2 surface area has 3,492 lbs holding it shut. Add 600 lbs spring seat pressure and multiply across a 1.53 rocker ratio, you have 6,260 lbs at the pushrod and lifter. Imagine jackhammering the pushrod, lifter, and cam lobe with the weight of a new F350, instantaneously, at 60+ times a second. You simply can't make a pushrod strong enough to withstand that. It would bend or snap just trying to open the valve. They have to wait until the piston is further down the bore, until cylinder pressure has lowered a bit more, before they can attempt to open the valve. When they have a catastrophic backfire, that lifts the intake and blower off the engine in a fireball, it's usually because something broke in the exhaust side of the valve train.