Well, AKG generally has a dry, clinical sound-signature. Very detailed, flat, accurate sound-stage, and due to this, not exciting, and definitely anemic on the bass. I can attest to this on the K701's. The 702's and Q701's you'll have to do your own research on to make sure, I haven't looked at cans since I found my perfect setup. To get the most out of AKG's, you'll want an amp.
The Beyer DT770's have very strong bass, but I'd argue too strong for many types of music. Plus, the midrange is less than neutral and the overbearing bass makes it even harder to distinguish. Lots of people attest to these for gaming, but I definitely wouldn't want them as an all-around can. The DT880's are more articulate than the DT770's and have much lighter bass. They are an open and airy sounding can. I don't think you'd be happy with the 880's. Beyers will also require an amp to get the most out of them. The low impedance 880's are one exception.
Sennheiser generally has a very laid back sound. Slower attacks and decays, warm, orchestra hall-like sound-stage, extended bass. The exception in the consumer line is the HD595 which Sennheiser released in response to fans wanting a more forward-sounding and exciting set of cans. The other exceptions are some of their professional studio cans. I cannot speak to the specific cans you listed. I have the HD650's which I use for classical and some ambient. You'll definitely want an amp with most Sennheisers. Some are OK without one, such as the HD555's, 595's and some others.
My suggestion? The Denon AH-D2000's. Great all-around cans and my go-to pair. Neutral mids, good highs, slightly tighter than neutral sound-stage (great for wide variety of rock and electronica), good attack and decay, good details. Also, the bass in my opinion is perfect. I definitely like my bass stronger than neutral but not crazy like the flab the 770's put out. It's extended and strong but not overbearing. Furthermore, they're comfortable and low impedance (work great even out of MP3 players).
Some reviews:
Denon AH-D2000 - Sealed Headphones| HeadRoom Audio Denon AH-D2000 Headphones Headphones review - Trusted Reviews