Is attack speed or AD better against structures
Turrets start with 40 armor which equals about 28.6% damage reduction.
Caitlyn at level 1 has 53.7 AD and .568 attack speed.
53.7 * .714 = 38.3 damage per auto attack. 38.3 * .568 = 21.8 DPS to a tower.
Add in a long sword you get:
(53.7 + 10) * .714 = 45.5 damage per auto attack. 45.5 * .568 = 25.8 DPS an 18.3% increase costing 350 gold (1% per 19 gold)
Adding in a dagger instead:
53.7 * .714 = 38.3 damage per auto attack. 38.3 * (.568 * 1.12) = 24.4 DPS a 12% increase costing 300 gold (1% per 25 gold)
Long sword is clearly the better option if you are limiting yourself to 1 item even though it is a bit more expensive.
TL;DR the longsword is the better option
For this example I'll pick a champion that does not exist but has a base attack damage of 55 and a base attack speed of 0.651. (These values are pretty much the average)
The turret we're focussing is one of the outer turrets. He has 3500 health and 45 armor (it has +5 armor after 6 minutes). This gives him an effective health value of 5075. (3500 * 1.45 = 5075)
Now for this calculations we will have minions to tank the turret (otherwise it'd gain more armor) but they will deal no damage to it. Since our champion has to kill the turret alone it would take him 93 attacks (5075 / 55 = 92.27...) to kill the turret. With his base attack speed he will attack once every 1.536 seconds (1 / 0.651 = 1.5361) meaning it will take him a total of around 143 seconds (93 * 1.5361 = 142.857) to kill the turret all by himself.
Dagger
Now the champion goes back buys a dagger and attacks again. The dagger increased his attack speed to 0.729 attacks per second (0.651 * 1.12 = 0.72912) which means he's attacking once every 1.372 seconds and thus will speed up the time it takes to kill the turret to roughly 128 seconds (1 / 0.729 = 1.3715, 1.3715 * 93 = 127.6)
With a dagger you're 10% faster than without items.
Longsword
A longsword will simply increase the base AD of the auto attacks meaning that instead of 93 attacks it now takes 79 attacks (5075 / 65 = 78.07) to kill the turret. With the base attack speed of an attack every 1.536 seconds it'll take the total time needed even further down to 121 seconds (1.536 * 79 = 121.334).
With the longsword you'll be 15% faster compared to having no items at all.
Note that if our imaginary champion had abilities that act as an auto attack reset, flat AD would be even better.