What is the difference between "largest" and "biggest"?
e.g.:
This is the largest bone
This is the biggest bone
Generally, they mean the same thing - more than average of size, amount, shape, weight and the like.
Though they mean the same, it depends on the context that whether or not you can use those words interchangeably. In your case, they mean the same.
However, if I ignore your example, and focus on your main question 'what's the difference between largest and biggest', I'd say that use them with caution. They are not interchangeable in all cases.
'Big' may also mean 'important' but 'large' does not.
Buying a house was the biggest
largestdecision I took this year.
There are many other meanings of 'big'. Also, these words are not used in some cases.
Good read is here on the BBC English Learning page.
Generally they mean the same thing and you should be okay interchanging them.
However, I offer a few counterexamples to add onto Maulik's post.
There are certain idioms that only work with one word or the other. You can call someone "big boned" if they are overweight, but not "large boned". However if you call a person "big" they could just be tall. You can be "living large" if you have an extravagant lifestyle, but you are not "living big".
Also, big can mean important. It is a big decision. He is a big person in the field.
Another case where they are not interchangeable, is when discussing the size of a product and in particular food and clothing. You can order a small or large drink, but you can't order a big drink (unless the drink actually is notably big). You can buy a shirt that is small, medium or large, but not "big".
In general they mean the same thing, other than a few isolated cases.
The two aren't always interchangeable in my opinion. Take this example. What is the largest lake in the world? Compare this to 'the biggest lake'. To my mind, the largest is the one with the greatest surface area, the biggest may have a smaller surface area but be deeper and therefore contain more water...and be 'bigger'. Of course, one could just as well assign the other way..but there IS a distinction. I think.