So what's the difference in flavor?
I'm not sure how this can be answered in a totally neutral manner.
I'll take a stab.
Mongoose Traveller is closer to Classic Traveller in its character skill levels, the task system, and in its relatively light core rules. Supplements add to the rules by topic, as needed, including careers. I've seen people mention that MgT feels like a cleaned-up and updated Classic Traveller. Nevertheless, MgT also attracts gamers from outside the Traveller fold, so it's not a grognards-only rule system.
Traveller5 is built around benchmarks relevant to Traveller games. As a result, material that would typically appear in a Traveller supplement (things ranging from environmental effects to robotics) is part of the core rules. There are also many "tools" in the core rules, using benchmarks, for building and describing animals, equipment, sophonts, and more. With these tools, the referee (and 3rd party publishers) can construct guns, armor, vehicles, ships, robots (and so on) which are consistent with the game rules. There are also generated examples for use out of the box.
Okay, that's my take, and I'm not very satisfied with what I wrote.