The way these two headphones are powered and connect to devices chiefly differentiates the two designs. The over-ear Monster Beats By Dre 'Studio' headphones run on two AAA batteries while the Sennheiser houses a rechargeable Lithium Polymer cell. The rechargeable battery in the Sennheiser 310BT is cost-efficient and powerful, helping to maintain usage over an extended period with both Bluetooth and noise reduction engaged.
Another small, but noteworthy distinction between the two headphones is the length of the packaged cable that comes with each. Again, the advantage here, even beyond its wireless functionality, is the more flexible 55-inch cable from Sennheiser. Monster only includes a 49-inch cable with the Beats By Dre 'Studio' headphones.
If you're primarily using the headphone to listen to MP3s or to connect exclusively to an audio player, the Sennheiser 310BT's offer a clear advantage in terms of portability, flexibility, and cost-efficiency. The only edge here for the Monster Beats By Dre 'Studio' headphones is the integrated smart phone controls to connect and disconnect phone calls.