Liverpool would be the only " BIG 4!! " team that I could see a legitimate argument for winning the PL being better then winning the Champions League.
For Arsenal, who have won multiple league titles in the last decade, I just don't understand how you wouldn't want to get your hands on the Champions League trophy above all else.
It's a better test of your ability to beat the other truly top teams, which I think is a better achievement than being able to consistently get the better of the likes of Hull and Blackburn every week.