Those are completely different concepts that are handled on different levels.
Mobile style: mobile browser is detected on server side and forum outputs appropriate style.
Responsive design: everything is detected on client side, forum outputs same content as for desktop browser.
Each has its own advantages and disadvantages.
Document size: that's biggest disadvantage of responsive design. Server sends same document as for desktop browser, so document might be quite large. It also affects loading time if your internet connection is slow.
Browser detection: that's major problem with mobile style. While most mobile browsers are easy to detect via user agent, many devices use standard user agent string or custom weird user agent string, making them hard to detect. List of user agents has to be maintained.
Screen resolution: width of mobile devices varies. There are small phones, medium phones, Galaxy Note, tablets. Mobile style will output minimum amount of information, which might result in wasted space on bigger devices. Responsive layout will change dynamically, working perfectly on all devices.
Same look and feel: mobile styles rarely look anything like forum's default style. Responsive design has same look and feel on all devices.
Both concepts are valid choices and they aren't mutually exclusive, though using both at the same time will require a lot of maintenance. So my vote goes for Selena Gomez.