I have run Traveller (Mongoose 2nd Edition) for just over a year, and as my game comes to a close I thought it would be worthwhile to note down some things from the experience. The below is no particular order, rather the order in which points came to me.

Simplicity:

Traveller is a surprisingly easy system to run. Although the rulebook itself is a tad dense, the set of rules you need day to day is small, and it's easy to express things in rules that aren't explicitly mentioned. Similarly, it's easy to "guess" what the rulebook would say and just go with your rulings. In the same vein, since Traveller has been around a long time and the rules aren't massively different from edition to edition, it's extremely easy to take an older rulebook or module and port it directly into the version you are running.

Character Creation is Great:

Character creation was really good. I feel like it creates an actual group that has a history and a reason to adventure. It also makes the usual session 0 style of play non-existent, since people are already familiar with each other's characters and have that sense of connection.

Psionics Aren't Great:

Since I was running my game in the Far Frontiers, which is mostly Zhodani influenced, my game had a lot more interactions with psionics, and overall I've come to the conclusion that they just aren't that interesting. Their combat implications are minimal, which leaves the more RP side of things, and most psionic abilities there are achievable in some other way depending on TL (apart from maybe teleportation). This isn't to say they aren't good in short bursts, but playing in an area that expects psionic abilities to be somewhat common meant that what few interesting tricks there were got used up pretty quickly.

Combat is Fun:

Combat is actually very fun. It has a lot more fluidity to it while still feeling tactical, which my players seemed to enjoy. They started as very non-combat focused characters who had to learn to survive, so combat was often about finding small edges and then finding ways to truly exploit them. Even once battle dress combat became a thing it felt like they had made an actual team that worked well together covering eachothers weaknesses and it had enough skill expression (both out of character and in character) that they go to do cool things the way that they wanted to.

Ship Combat is Meh:

In our year-long campaign I believe we ran combat in space three times. Of those three, I would say that only one was truly engaging from both a GM and player perspective. The other two devolved into both sides performing the same set of actions over and over until one side folded. This may just be a symptom of the ships involved being small and having limited capabilities, but as a GM I would only ever run ship combat again in the context of something more interesting. As an example, the one interesting time was attempting to flee another ship with intruders onboard and a semi-broken flight computer. The resulting mess meant there were way more options and things going on than "I shoot you, you shoot me".

Balance:

Traveller comes across as a game where balance isn't really the intent. I think this is on the whole fine. What your character can do in session 1 and session 50 is pretty similar, and this similarity opens up a lot in terms of gameplay. In general I found that it led to a lot more complex planning, and executing a well thought out plan almost felt unfair to the enemy. Of course this is fine and goes both ways: the players feel powerful when they have the time and the resources to do what they want, and when they don't, it always feels possible that someone could die.

The big exception to all of this is money. Characters may not change much from session 1 to session 50, but their bank balance can. Trade is a very good way to make money in Traveller, to the point that I ended up writing a separate post on it. The short version is that a party with a ship and someone with Broker will end up with a lot of cash, and that cash has to go somewhere. In practice it means more expensive gear, and more expensive gear means more combat capability as mods and the like start getting used. Before you know it your average characters will be souped up with truly lethal gear, making the average military unit a significantly smaller obstacle.

The Sandbox is Massive:

I would argue that the best part of Traveller is having so many places to visit. My campaign ran in the Far Frontiers, which is admittedly a rather sparse area in terms of official content. That said, most planets have more than enough to add colour to what you are doing. I found it extremely easy to find launching points for problems by just reading a little about the history of nearby planets and taking things to the extreme. Obviously you can make your own sectors, and I think that can be fun as well, but there are so many Traveller worlds that you can find a place that suits whatever kind of game you want to run. Having stuff like Traveller Map makes it much less stressful to ask the question "where do you want to go?", and it feels more like players are making informed decisions about what they are doing.

Travel Lag:

News only travels as fast as ships do, and this travel lag ended up becoming a bit of an important plot point at times, with the party evading news of bounties and the like. This does add extra burden in terms of keeping track of when certain bits of information get to certain places but when its important it does add an additional bit to how you plan to get to places.

Getting the Campaign Moving:

I got my group hooked up with "The Problem Solvers Initiative", which was basically a mysterious org that had them doing small jobs that later turned out to be part of larger political maneuvering. This slowly got them coming up with their own goals, which made things a lot easier. I found that once the party had a few allies and a couple of clear nemesises I spent less time coming up with hooks and more time thinking about how those NPCs react to certain actions which in turn leads to more interesting sessions.

Prep is Light:

My prep burden was 2 hours per week at most, if that. Given how sandboxy it was, at times I wouldn't prep anything and would just improv my way through the session, hoping to end up somewhere with a clear direction for the next one. Although at the start it really did feal a lot more daunting. The size of the explorable space is imense. What I would recommend is that for the first 2 or 3 sessions keep it to a single planet, this makes it far easier to get into the swing of how traveller sessions tend to go.

Final Thoughts:

I really enjoyed running Traveller and would run it again with a few mods, mostly the ones mentioned in my trading review. I think it will likely work for people who want to try sci-fi and are not looking for the traditional power fantasy in their games, and are ok looking up the procedures from time to time.