The Penguin editions are great. Accessible and largely respected (if you're using them for academic citation).

I've been relying on the Loeb editions and they seem to be still widely used for teaching purposes. Only the Secret History has more modern translations anyway - one by Peter Sarris for Penguin (I think he just updated an older Penguin translation though), the other by Anthony Kaldellis. Both are excellent historians of this period so their introduction/notes are both very useful. Sarris' version is very readable, whilst Kaldellis goes for authenticity and reads less well in English (in my opinion). Kaldellis has also done an updated translation of the Loeb version of Wars in 2014, published as The Wars of Justinian, but I haven't taken a look at it yet; the translation seems to be largely the same as the Loeb one, except now it is has modern footnotes and maps to go with it.