Between Mongoose Traveller and CT? Lots of little stuff, really. The two should be able to share subsystems in some cases.
Also keep in mind that Mongoose Traveller (MGT) is at three books at the moment, and those three are the topic equivalents of CT Books 1-3 and Supplements 3 and 6.
*The fairly casual task resolution system of CT is pinned down and defined a bit in MGT, but the two are quite compatible.
*Weapon and armor handling is a hit-or-"miss" system in CT, and a damage reduction system in MGT. Gotta pick one, as they don't mesh particularly.
*All character generation is at a single level of detail in MGT, while CT has the Basic Careers of Book 1 and Supplement 4 and the quite different Advanced Careers of Books 4-7. The results are mechanically compatible across the three options, but give differing skill densities.
*MGT ship building currently stops at 2000 tons (but will extend past that soon) and includes options that were not in CT Book 2, but is otherwise at a Book 2 level of complexity (ie. not very).
*Ship combat is currently "Roleplaying" scale only in MGT. Fleet scale is coming.
There are nuances and other differences, but that's the stuff people tend to notice first...