Much more transparent indeed. Bridgestone has closer ties to the organisation and can get things done. Pirelli has to get all the teams and the fia on the same page to push through changes.
The biggest issue is that bridgestone did not take a surface imprint of the new surface. It only sent some inexperienced engineer over to have a look. Concerning the approach towards the australian event, they were sluggish, even lazy. Overall bridgestone did a very good job over the years, but on the other hand they can't afford the same mistakes as pirelli makes in F1. If pirelli instead was in motogp and made the same mistakes as in f1, the consequences would have been disastrous. A delaminating tyre will 100% guaranteed end in a crash in motogp, and chunks of the exploding tyre will very probably hit the rider behind. And when somebody dies from that, pirelli would still have the nerve to blame the rider.