EDIT: This brings back good memories. I'm one of the few that actually liked the 2300 AD rules system (I did have a key combat house rule that didn't change the outcome or balance while making the system greatly easier to run). I would still be playing 2300 AD instead of Traveller if it wasn't for missing key elements in the setting - No large area for the players to run about in being Mercs, Traders, whatever they wished to be. The setting limited what the players could due, it wasn't as open-ended to players used to Traveller.
As Peter pointed out, most worlds in the 2300 Colonial Atlas are actually not very well exploited, many aren't even very well explored. There's a note somewhere in the 2300 book that most of the colony worlds listed actually have enclaves and similar "smaller" (10,000 people or less) that aren't mentioned or listed in the supplements; you can easily put in even larger communities on certain Frontier worlds without appreciably influencing the "canon" of the Colonial Atlas (should you wish to follow it to the letter).
Trading, beyond certain concerns about getting products up and down the gravity well, is very easy to do in 2300. In fact, given the greater detail in the Colonial Atlas, it's actually much easier to determine what products are likely to sell without dealing with Traveller-style generation charts for commodities (I don't know what to tell you if you actually liked those charts, though).
Exploration of totally unseen worlds is actually
more possible in 2300 than it Traveller, I think. Once you get over the big hurdle of getting your own ship, it's really not many weeks journey to get to the end of an Arm into unexplored space; likewise, it's not so hard for players who absolutely adore the "exploration/contact" stuff to sign aboard the
Bayern.
Mercenary work is a little iffy. In theory, the Kafers and the war on Aurore and the events of
Invasion and the second invasion of the 2320 timeline should give players all the mercenary work they could ever hope for. Mercs are in high demand due to the Kafer War. The problem, of course, is that Kafers are aliens and once you get their schtick down, they're simply not as interesting to fight against as other humans. Sad but true. However, if your players aren't the kind who want to go blazing into combat with missile-tossing RPVs, hovertanks hosing everything that moves down with plasma gun fire, and combat walkers stomping over what's left, there's actually plenty of "lighter touch" mercenary work to be done - again, the CA and similar supplements for 2300 pretty much write such adventures themselves. The entire concept of "Troubleshooters" are pretty much mercenaries who are empowered with pretty much carte blanche to investigate and resolve problems out on the Frontiers for corporate and governmental officers in the Core. Possibilities of tangling with disgruntled colonists, criminals, wildlife, weird alien artifacts, and of course, other troubleshooting teams are pretty much endless. If you want to play the "darker" versions of 2300 (which I partially did) you can have all sorts of nail-biting scenarios that the more believable nature of the tech in 2300 makes possible.
For instance, I had a pretty stock scenario where a Trilon agricultural enclave on some Frontier world had stopped transmitting. Orbital photography showed very little activity at the colony site and that the cargo containers filled with supplies that the RPVs dropped off periodically were just lying where the retarding parachutes had left them. Local law enforcement had sent in some people, but when they hadn't returned the French government complained to Trilon. Trilon hired the players as experienced troubleshooters to go in and investigate the problem and see what was going on. The players arrive after hitching a ride on a fast courier going to Kie-Yuma that drops them off.
The players eventually find out that the sprawling agri-colony made an ideal smokescreen for the Trilon bioweapons division that was testing out drugs designed to suppress the Kafer intelligence reaction with the aim of actually making people dumber temporarily as a method to increase worker productivity and population control. The result was a spontaneous "species jump" of human bacteria to Kafers, which then mutated in the Kafers again and reinfected the humans, leading humans to react by becoming feral and utterly sociopathic and homicidal. When the Bioweapons team learned the Agri Division had already sent troubleshooters out, they in-turn sent out their own merc team with orders to ensure the players didn't find anything and if they did, that they were not to return. They were outfitted with biological protection and diagrams of the agri-combine's biogas reactors so they could create an "enhanced conventional detonation" that would wipe the site out (after they had retrieved whatever data they could). Unbeknownst to Trilon, the French government had sent out an intervention team of gendarmes as well to investigate the deaths of French law enforcement in the area as well...