If $2.7bn over 6 years is correct that puts the deal at $450m a year which is slightly crazy as that is $1.18m for every game in a full season of 380.
To put this into perspective the NHL can have up to 1312 games per season, as you've 32 teams play 82 games, then have a play off system of 16 teams that can play up to 7 games each round. That means the NHL deal is valued at around $476,371k per game (this however, isn't a strictly like for like basis, as there are blackouts for local areas and other conditions on the NHL deal rather than open to all; although equally I guess it could be said that the PL games are also not equal as most games are tucked away; additionally the playoffs never get maxed out series.)
Then you compare this to the La Liga deal, which is $175m a year but that is over 8 years. That means the PL deal is worth $1.3bn more over two less years or $2.2bn more if you say that there isn't any room for growth (unlikely) in the next round of rights.