I have never played any Traveller, however I have found an RPG.net review, on which I base my answer.
- Size: 2nd edition has 60 more pages.
- The art: 1st edition was made in 80s style. 2nd looks more modern, with a great layout and adequate art. There are lots of illustrations.
- The base system: Now includes both positive and negative modifiers. Opponents skill levels/defense values subtracted from the one roll. Opposed rolls are kept to a minimum. The target number for success can range from 4 to whatever.
- New mechanic (Bane/Boon): you roll 1 more die, and drop either the highest or lowest roll before determining total
- "Academies" It gives you a lot more control over your first term as you get to select skills rather than roll randomly. If you graduate, it guarantees your entry in your career of choice.
- Jack of all Trades: The skill that can be gained ONLY during character creation.
- Skills: They have been grouped into specializations to remove skill bloat. There is also a nice description under every speciality.
- Dual wielding available
- Encounters & Dangers: Whole section has been improved and detailed.
- Equipment: Needed explanations have been added. Armour have been optimized. Their values and costs now make sense. Augments, that boost your abilities have been added. Communication and Computers/Computer software section has been updated and clarified.Weapon section has been upgraded.
- Vehicles: Are described by traits and hull values. There are Speed-bands for the vehicle speed. Lots of new rules have been added.
- Spacecraft operations and combat They have taken a new, better approach.
- Psionics: Has been revised and detailed more clearly. It has also become more helpful.
- Trading: You can no longer sell for 400% of base price, it is limited to 200% now.
