Depends if you're happy to spend a relic on the Company Champion. If you're already doing that, you can give a relic to the Emperor's Champion too to even the odds, just not that same weapon I guess. Otherwise, the two aren't on an even footing for comparison.
Outside of relics, the only thing the Company Champion has better than the Emperor's Champion is that he can fight first. The Emperor's Champion, on the other hand:
- has a better standard and invulnerable save, even if the Company Champion has a combat shield;
- has those rerolls;
- has +1S on the sword
The damage on the swords comes out as an average overall, 2 compared to D3.
Personally, I'm not sure I would want to spend the free relic or the CP on giving the weapon to the Champion - perhaps if you're regularly up against big monsters, like Daemons or Nids.