Players use Lifesteal gear on there CB team because it lets there hero stay self sustained.
You can get full heals when ever you do a Warmaster or Giant Slayer Mastery Proc.
This means you don't need a dedicated hero on your team to keep the rest of your team alive.
Players use Stalwart gear on there CB team when they have a dedicated hero.
A dedicated hero is designed to keep your team alive.
You often need a very powerful Healer or Shielding champion on your team to pull this off.
The Healer/Shielder can keep your heroes full health during the fight so you don't need Lifesteal gear.
You can use Stalwart gear to reduce the damage your heroes take from the Clan Boss.
Just to give you an example:
Bad El Kazar is a Legendary Champion people often use in Clan Boss.
Bad El Kazar does very good heals on his A1 + A2.
Bad El Kazar can keep your team alive in the fight by himself.
The goal in Clan Boss is to stay alive for as long as possible.
Most players aim for 50 turns.
If your team stays alive for 50 turns in the fight, You will often put out some very good damage.