You can see for yourself the changes to the "Hub and Spokes" rules, as they are the first 90 pages, and are included in the preview at http://www.burningwheel.org/?p=276. Under the word "Here" in the fourth paragraph on that page is the download link for that preview.
Luke has mentioned that there are numerous small changes to Fight, specifically the processes for range setting, Duel of Wits, and Range and Cover.
Sorcery no longer adds will dice to rolls to cast, reducing the difficulty of advancing Sorcery as one no longer needs insane Obs to get Difficult and Challenging expenses.
Perception is no longer open ended.
Let it Ride drops the bit about referees cheating.
A significant change in terminology: "Graduated Test" replaces the older "Open Test", avoiding the frequent confusion between open ended rolls and open tests.
Some minor changes to the difficulty/test type table at the low end.
Many lifepaths have been revised.
I've not yet gotten BWG yet, only the preview, so I can't be much more detailed, but I'll note that the hub and spokes text is not readily different at first glance, but some small changes are present.
References
http://www.burningwheel.org/forum/showthread.php?11076-Burning-Wheel-Gold-Errors-and-Changes
I have not played either, however there is a thread on RPG.net that discusses many of the same things: The RPG.NET thread on the topic
However, on reading it only the first comment is useful to you, so I am going to quote the relevant parts here:
Troubleshooters is the 25th Anniversary edition of the Mongoose 2004 PARANOIA rulebook (formerly known as XP). There are minor tweaks to the rules, but it is basically the same game. Likewise, the companion Internal Security rulebook uses the same system, though there is extensive new material there for BLUE-Clearance IntSec missions. Neither is mechanically complex, and both place unique emphasis on the Gamemaster's supremacy. Every rule in both books exists as a non-mandatory advisory to the GM's incontrovertible authority.
In contrast, High Programmers is a completely different game with an unusual and innovative rules system. It isn't necessarily complex, but the players have more options and hence a greater cognitive load than in Troubleshooters or IntSec.
Each book offers copious advice on designing missions, plus pregenerated player characters. Troubleshooters, in particular, adapts the XP GM Screen's "mission blender," a collection of tables that lets you generate an entire mission randomly with the roll of a mere five dozen or so d20s. Troubleshooters also includes Ken Rolston's classic introductory PARANOIA mission "Robot Imana-665-C" as well as a fine new mission by Gareth Hanrahan, "The Quantum Traitor." High Programmers includes one mission, "Disaster Management."
— Allen Varney, 04-16-2010
Other comments in that thread indicate that the Official Paranoia Development Blog has information on the designers goals with each system.
I hope this helps, it seemed a shame to have this thread with no answers for so long.
Best Answer
Here are the most important changes off the top of my head.
Starting Archetypes are now largely fixed.
The amount of customization you get to do on your beginning character has been drastically reduced. To more or less zero for most Archetypes (AT) in fact.
Attributes have been eliminated
Remember Mind, Body, Chi and Reflexes ? Well, forget'em. Your Skills, Attack and Defense values are now fully independent. Chi and its' secondaries still exist in concept as each AT has a "Magic / Luck" stat with names reminiscent of the old ones, but they're no longer linked as they used to be.
There's no such thing as XP.
Gone. Poof. Character progression is now managed in discrete units called Advancements. Once you've gotten attuned to your first Site, you get your first Advancement for free, with which you can buy from a selection of schticks, skills and other character options defined by your AT. Further advancements are earned with a die roll made at the end of each session, the odds of which increase the longer you've gone without advancing.
The world has Changed, capital C.
You'd think this goes without saying, but really, changed deserves to be triple-underlined in thick sharpie here. Just to begin, the New Flesh is no more. Thanks to the thoughtless actions of the Jammers, the Future juncture is an honest to goodness Fallout-style wasteland, complete with Chi-mutants and scavenging road gangs. The Ancient juncture now links to 690 CE, where the Lotus has drastically weakened... The Dragon are still screwed though.