Hallo all, it's been a long time. I'm cycling back into a Traveller phase, so this question seems like an appropriate place to re-enter the fray.
I was among MGT's most bitter critics when it came out. However, as I saw Mongoose attempt to make a credible product, I softened a lot. In particular, Mongoose impressed me with their willingness to move quickly to fix major screwups. And I even wrote a few downright nice things about some of the supplements. I mention this to declare my biases.
I would play CT over MgT for several reasons. The biggest reason -- which is inapplicable to new players -- is that I have 31 years of familiarity with CT.
The second biggest reason is that I really can't think of anything important that MgT does better than CT. Yeah, I know about the task system, but I just can't get too excited about that. Since the early days of CT, we've been buried with various task systems. IMHO, all this effort was expended to solve a non-existent problem. And for cripes sake, let's give it a rest.
This is not to say that CT is perfect. Far from it. For decades, I've used an alternate combat system. Books 4-6 produce*(IMHO) absurdly overpowered characters and I have had to fix that. Book 4 weapons shatter the CT combat system .
But CT was simple and elegant and allowed for easy modification. The problems that I perceived were easy to fix and I did so. I lack the patience and time to do the same for MGT.
The good news is that the two games are sufficiently similar that MGT can be a decent resource for CT referees. However, many liberties are taken with CT canon, which can be irritating.
CT was also written by serious wargame designers, so its military elements were generally very well done. Many MGT authors seem to lack such a grounding and it shows. (That said, Matt Sprange is a fellow wargame grognard).