It depends.  On some DEF champs, attack is based on DEF.  In that case, any Offensive set bonus is wasted.  Also any weapon, regardless of set,  has ATT as the primary state and is likewise wasted, but the secondary stats is what you choose the weapon on (You have a slot for weapon, might as well benefit from the secondary stats).  Any other artifact that boosts ATT is wasted.

Defense based characters do damage bsed on their defense ( in the majority of cases ), some Defense champs will scalle off of HP as well or other stats ( if it's the case it will be stated on the champion skill description )  For your example : Atk% boots from the defense set are not good on a defense champion,on the other hand Def% boots from the attack set are much better ( but still not optimal ) 

You're only half right. Atk stats on a champion whose skills depend on Def or Hp are utterly useless; however, all champions benefit from Def regardless of what their damage scales off of since it mitigates incoming damage.

Any defense stat is welcomed on every champion . Attack base champion or otherwise

A defense based champion (look at their skills and this will say damage based  on DEF). Will not benefit from any attack on any artifacts, be it attack % or flat stats.

So when I look for artifacts for my Defense based champions I try to avoid any primary or sub stats with any kind of attack (as stated your weapon will always have a primary attack stat which cannot be helped)

Thanks for the answers all, so in that particular case it would be silly to put that piece on a pure DEF based champ, Rhazin for the sake of example, because I'd get the Defense set bonus but completely waste the primary stat. But it could still be useful on an ATK champion (say Elhain), because she would benefit from the primary stat but also from a defense set bonus to keep her alive for a little longer. 

That makes DEF champions harder to properly gear, no? They'll never benefit from the ATK stats at all, while ATK dudes still benefit from DEF, if I get this right🤔

I love DEF champions and gearing them. The more Def you give them the better they are able to deal damage to the enemy and the stronger they become against enemy attacks

Be sure not to forget crit rate and crit damage for that extra damage effect

Agreed they seem pretty efficient, I actually survive in the arena almost solely on DEF and HP. I just have a hard time finding proper gear it seems. I get very unlucky pulls and yet I got Scyl sitting in my vault for lack of a proper dress to put on her :) I gotta say I don't know how you guys do it to at the same time get decent ATK/DEF stats, AND critical rate, AND crit damage, AND accuracy and resistance 😂. 100% free to play here, but even so...