These headphones offer me a lot of flexibility of use - both in recording and mixing. They're exquisitely well-made and have a great sound. For mixing and mastering purposes you'd do well to consider the 880s and 990s, as their semi-open and open nature suits the task better. However, for my current situation where I need a set of headphones to fit both roles, these do it to perfection.
I've been looking for a set of studio cans for a while, and have always heard amazing things about the 770s, 880s, and 990s. Initially I was having a hard time figuring out which one of those would be best for me. I wanted a pair of headphones that I could simultaneously record with (meaning, with minimal spill), and that I could mix and master with.
After a bit of EQ I got them to sound more natural and a bit more neutral. The 770s have a bit of a fame for strident highs. While I don't exactly agree that it is overbearing, the higher frequencies did indeed carry an extra power, which is something I don't have a particular taste for. After running some tests, I EQed them to taste by raising the lower frequencies by just a bit, as well as lowering the higher frequencies. Just a touch of gain adding and reduction here and there, and after that, they were good to go for me.
One word of warning for you is to really check the impedance for your needs. The 250 Ohm version is reported to have better clarity especially when it comes to dynamics transparency, and needs to be amped properly. For mobile day-to-day use, the 32 Ohm version would be your best bet, easier to amp to get you to where you want to be in terms of volume, at the very slight cost of detail. As for the 80 Ohm version, that one is usually selected for recording musicians (say drummers) who need a bit of extra volume for when recording louder instruments.
Either way, the claims of quality from everyone who recommended a pair Beyerdynamics are definitely well-founded.