Ive listened to the Q701 and DT880 recently, among other headphones...
I would say that while Q701 do have soundstage that is very nice (though not perfectly as developed and deep as with the Senns), their tonality is a little bit off (they lack subbass and have hearable strange 2khz emphasis). DT880 are more neutral than Q701, except for very strange Beyer's typical emphasis of frequencies around 10khz which makes especially drums sound exaggerated all the time. It may sound like its not a big issue but for me, it definitely is... That emphasis is hearable all the time once you start to analyze. Soundstaging of DT880 is not as good as with Q701, though not bad at all considering their price!
One headphone I was really satisfied with FR wise were HD598. They are really balanced and quite HD800-like here, its their strongest feature. On the other hand, they definitely lack soundstage and overall quality so rather not take that route.
I can honestly tell you that you should listen to Q701, K712 Pro and DT880 yourself and decide which one to choose. But I am worried that none is gonna deliver a versatile and complete experience of HD800.