Nuts can be one of the healthiest sources of fat for humans, and it also can be not so great if you choose the wrong nut. Nuts can help you lose weight, or it can make you gain weight.
While they're all high in fat, low in carbs, and have a moderate amount of protein, what types of fat and what types of phytonutrients they have is different.

So which nut has the best most anti-oxidant rich anti-cancer profile?

To find this out the best way to determine such a specific thing is to look at total anti-oxidant content of each nut, as that's the primary difference between these nuts that would make them better at fighting cancer and disease.

We will be looking at the ORAC value, the value at which the phyto-chemicals absorb/neutralize (Oxygen) radicals or to translate this into more familiar terms: the total antioxidant capacity of each of these foods.
The study in which I will be using can be found here.

As you can see for yourself, looking for the highest numbers in the "Total ORAC" data field, there's a clear winner, and that winner is Pecans.
They're closely followed up by Walnuts, then things start dropping more significantly with hazelnuts and pistachios coming in 3rd and 4th place, followed by almonds, then peanuts, cashews, macadamia nuts, brazil nuts, and coming in absolutely last with almost no anti-cancer properties, regular ol' Pine nuts with over 29 times less anti-oxidant power as oh so wonderful Pecans.

So the clear winner to who is the best nut to protect from cancer is Pecans, and if you don't like them slumping down to Walnuts is a non-issue.
Funnily enough Pecans have not so great Omega-3 to Omega-6 ratios, so on the basis of overall health it may be more advisable to consume Walnuts due to their far more acceptable ratios.