AD or Ap

I would say AD usually, since that is also mostly matched with attack speed

depends...

Veigar will shread towers super easely with his 1000+ AP

attack speed champions shred turrets the fastest

all eat turrets for breakfast

You deal 40% of your AP or 100% of your AD per auto, depending on which is higher.

So a Level 18 needs more than 265 AP before he'll start dealing more damage to towers per auto attack than he would with no items.

In contrast, a level 6 with a deals more damage per auto to the towers.

Combine that with the Attack Speed that AD Champions typically have, and hands down AD is better for taking towers.

In general, ADs should be faster at burning a turret if left alone because they are likely to have higher attack speed and build more of it in items/runes. There are obvious exceptions like those who build ( ) or those with extra turret damage in their kits (). For discussion purposes, let's use Ashe and Xerath as our two champions. Different champions will have vary somewhat based on different base AD/AS values and what items they want to build.

Level 11 AD = 76 + 8 + 70 = 154 AD AS = 0.658 + 29.2% + 40% + 35% + 20% (approx from runes/masteries) = 1.48 AS DPA = 154 physical DPS = AD * AS = 228 physical

AD = 81 AS = 0.625 + 11.9% = 0.70 AP = (15 + 100 + 120) x 1.35 = 317 DPA = 81 phys + 158.5 magic = 239.5 total DPS = (AD + 0.5 x AP) x AS = 56.7 phys + 111 mag = 167.7 total

Level 18 AD = 95 + 70 + 50 + 75 = 290 AS = 0.658 + 56.6% + 40% + 35% + 20% = 1.66 AS DPA = 290 physical DPS = 481 physical

AD = 106 AP = (100 + 120 + 100 + 80) x 1.35 = 540 AS = 0.625 + 23.1% = 0.77 AS DPA = 106 phys + 270 magic = 376 total DPS = 81.6 phys + 208 magic = 289.6 total

This is already long for a forum post, so I ignored things like red/blue buffs, elixers, etc. I also didn't account for the effect of penetration. Mages will generally have a fair bit of magic penetration in runes, boots, and eventually Void Staff. Note however, that this only affects the magic damage portion and not the physical portion from base AD. Marksmen will generally have Last Whisper (which may or may not help, depending on if turret armor is "bonus" or not). Flat pen on marksmen is generally rarer, but the current trend for some marksmen to go with the flat armor pen items does help them with turrets.

You'll note that Xerath has a higher raw damage per attack to the turrets than Ashe. This means that if you can only get one attack off at a time during a siege, then attack speed is basically irrelevant, and Xerath is actually "better" than Ashe at taking the turret.