You keep saying Varus is better at busting tanks than Ashe. Are you sure about that?
I'd assume you think he's better because of his W, since claiming his other abilities help him to bust tanks make very little sense. But how much damage does your W actually deal to tanks? At first 15% of their HP as magic damage might seem very high but when you stop to look at numbers you see that tanks reduce this to a very small sum of damage.
VS a tank with 4000 HP, 308 Armour and 200 MR (I think we can agree these are fair numbers) how much damage does your W deal? It's got a base of 600 magic damage after 3 autos, but the tank you're hitting has MR to reduce your damage. You only end up hitting for around 200 damage. With a standard ADC build your W adds around 678 raw magic damage every 2 seconds, or 112 magic DPS assuming you proc it every time it has 3 stacks.
Do you know how ADCs not named Vayne melt tanks? With physical damage. You're AAs (still Varus) bring in 875 raw DPS, mitigated to 289 damage by armour (after pen). You're Q (uncharged as charging reduces DPS from AAs) and E add a combined 98 DPS mitigated to 32 by Armour (I'm counting these as DPS and not burst as you can often use them a couple of times on beefy targets, plus if used to try to burst you lose most of your W damage). Your ult adds 350 instant magic damage, mitigated to 116 magic damage. I'm including SS in the build but only giving one proc because it's very hard to factor multiple, It adds an average of 168 magic damage, mitigated to 55 magic damage.
Varus's damage equation against the selected target is D=171+433T meaning through this model it would take Varus about 9 Seconds to kill a 4000 HP target assuming he procs his W every 2 seconds, which is rarely possible. He can trade some DPS for burst but it would cause him to take longer to kill the tank.
Ashe on the other hand has a higher AS meaning she gets a higher physical DPS. Ashe deals 1002 raw DPS mitigated to 334 damage. Her W adds 106 DPS, mitigated to 35 damage. Her first auto is a 100% crit, meaning her SS burst is 250 damage, mitigated to 83 damage. Her ult deals 600 damage, mitigated to 200.
Ashe's damage equation against the selected target is D=283+334T meaning it will take Ashe around 11 seconds to kill a tank. This does not factor Ashe's 100% crit damage however.
A 2 second difference here really isn't that big. Compared to champs who can't shred tanks like Ez or champs who specialise at it like Kog, Ashe and Varus have very similar abilities to melt through tanks.
There's also the fact that Ashe deals the damage more safely that Varus, generally earns more gold and has more items and brings far greater utility to a team than Varus can. I don't even think that a standard build is best for Varus, I'd generally consider Legolas build better and that build can't kill a tank to save its life.