In an overall Windows user experience? Definitely moving windows between screens. Selecting tabs is a pretty niche and uncommon feature across the OS.
It's not about which action is more common, its about the fact that the titlebar drag gesture is universal cross windows 7/8 and is a key element of the user experience.
There are exactly two apps I've used in the entire history of windows 7 that broke this interaction: Chrome and FF. The fault is on those browsers breaking expected behavior, not Opera for doing what windows users expect. The FF UX team admitted that they overlooked this but its understandable that they're keeping it as users have come to expect it.
Multiscreen usage is exceedingly rare, except among hn readers. Among that crowd having lots of tabs open is the norm. So, the subsegment of multiscreen users who don't use a lot of tabs is probably vanishingly small. Myself I'm a windows user a majority of the time and I strongly prefer chrome's behavior.
Another thing lots of applications with custom title bars get wrong: double-clicking the top-left corner of the window (where the icon is, usually) should close the application. (Firefox is an offender here, too, though Chrome is not.)
I had no idea this is a thing, which is.. surprising to say the least. That explains a lot of what I thought were crashes, but wow is that user hostile.
I'm really hesitant to say Firefox gets it "wrong" even if it is inconsistent.
Why not have a way for the window to convey to the window manager that it (the window) is primarily just a holder of tabs (as most browsers, and increasingly more applications, seem to be), and let the WM decide based on the user's preference what the correct behavior and display is?
Is there still not a single window manager that understands tabs as a first class object? Why does Chrome (the browser) give me all sorts of fancy tab-related features, but no other program does? Even Windows nearly got this right back in the 3.1 days of MDI, and the entire world has regressed since then.
Because window manager is hard to extend and hard to customize . I can trivially change this and lots of other things in Firefox, but with windows WM i would have to wait 3 years to get any bug fixed or a new feature added.
Also calling chrome or Firefox window "just a holder of tabs" isn't fair, they are very special holders of very special tabs, and lots of work goes into them to make them work properly. Also there are other "holder of tabs" windows, e.g Sublime Text, which are mostly similar but have important differences. Trying to move all that complexity into WM simply won't work.