Well, Tesla T1.1 is DT880-like in terms of soundstage although significantly improved in terms of layering and focus. The soundstage is rounded, not very intimate like HD600 and not distant like HD800. Tesla T1 is slightly warmer than DT880 and some pairs are tuned similar to AKG K7-series in the upper midrange, giving vocals a more upfront presentation without sounding nasal (like some of the K7-series). Overall the Tesla T1.1 is more organic sounding than the DT880 and technically superior across the board. An important difference to keep in mind is that the T1 is a little bit more laid back than DT880 which appears as more energetic especially around the 6kHz region.
HD800 is similar to DT880 Pro in terms of sound signature, it's quite dry and clinical with slightly recessed upper midrange and great extension at both ends of the spectrum. Soundstage is very different from DT880, HD800's soundstage is very wide and the ring radiators project bigger and more distant objects. Transparency and precision across the spectrum is top notch.
HD800 is a technical monster but you have to trade the warmer and more organic sound of the T1.
Both are a step above the DT880, but your preferences and desired use play a big role when deciding which one to pick. Tesla T1 is a more powerful tool than DT880, but it's also tuned towards musicality and that's why is so highly regarded as an all rounder among reference headphones. HD800 on the other hand is more of a dedicated precision tool (less bass, drier mids, more treble, wider stage) but it won't convey musicality with a wide range of recordings.