I've never really understood how it's easier for big teams. Unless you ended up in a group of death, the group phase usually guaranteed a route to the last 16 for any half decent team.
The Swiss format provides a bit more of a safety blanket, but it also significantly increases the chances of lesser teams to accumulate points. A team like Brest would have had no chance, now they have an excellent chance of a CL knockout game and with a bit of luck with the draw, a CL last 16 place.
I was always open minded but I'm convince now that this format is better.