I played what we now call "Classic Traveller" back in the 80s. When I decided to start a Traveller campaign I started researching all the versions to figure out which one I would use. I selected Mongoose Traveller and here are the reasons:
Classic Traveller:I have many fond memories of this, but thought that after all this time it might be showing it's age a big. And while it is still awesome I no longer have any of the books and figured it might be time to move on. Therefore it became my "safety net", if nothing else was any good I always had this to fall back to.
MegaTraveller: Despite not being thrilled with the setting, it just looked to darn complicated. It's like they took everything that anyone ever thought might be missing from the original and tossed it in there. So it went from simple to ridiculous.
Traveller: TNE: Quite simply I couldn't find much on this one and what I could find wasn't very positive.
Mongoose Traveller: This came across as an enahanced version of Classic, but not with all the stuff that MegaTraveller added. It was somewhere in between and it kept a lot of the flavor and what I loved about the original. It moved to the top of my list quite quickly. The fact that you could still purchase books new was a big plus as well.
T5: I had high hopes for this. I was excited when I found out about it. Then I started reading reviews and while there was nothing bad about the actual game play and the system, what people were saying about the book scared me. It was poorly organized and HUGE. And at 700 pages there was no doubt about the HUGE part. I was able to get a look at the book as well and the reviews are right. Trying to follow what is going on in that book gave me a headache.
So that is my 2 cents on each version from the research I did. The other thing I like about the Mongoose version is that it is close enough to Classic that I can use stuff I find that was written/designed for Classic and pretty easily modify it for use in Mongoose.
Of course I also just found out that another patron of my local gaming store happens to have a large collection of Traveller books from the 80s (I am assuming mostly Classic) and is looking to sell them. He is going to send me some pics of what he has and we are going to get together at the store this week. So I might be shifting things more to Classic...