The new edition of Third Reich is significantly different than the last published AH edition. In no particular order:

The land CRT (with its dreaded 1:36 possibility of an A-Elim at 2-1 odds) is gone. Instead, you roll a small handful of dice (basically, one for each combat factor) and inflict "hits" on opposing units when high numbers are rolled. Hits are taken by eliminating units, flipping them to reduced strength or paying BRPs. The attrition CRT is also gone.

HQ units have been added, and instead of buying options for an entire front, you buy HQ offensives that permit the units within range of the appropriate HQ to move and attack. Some nations can buy "General Offensive" chits that permit multiple HQs to be activated. There are also Naval and Air Efforts chits that can be purchased. The turns are still quarterly, but all the purchased chits get dropped in a cup and pulled one at a time. After enough chits have been pulled, there is a die roll made to see if the turn ends.

The naval and air systems have been touched up a bit, with the major difference being the creation of sea zones for resolving naval combat. The focus of the game remains on land operations.

Strategic warfare is now resolved turn-by-turn instead of annually. The counters are more colorful than the AH ones, and are now two-sided.

The map has been reoriented to show more of Scandinavia (up to Narvik) and loses the vast empty stretches of the USSR around and beyond the Urals that never saw play anyway. The map is mounted, and uses color rather than plain white for clear terrain. The hexes are small, and manipulating the counters on the board can be awkward (have tweezers handy).

Overall, I think the game was worth buying. I like most of the changes, but a lot more uncertainty has been introduced. If you prefer a more chess-like battle of wits, this version might not be to your liking. The counters are definitely better, but I frankly think the board is bad. The small hex size makes things hard to move around, and the one I got was warped badly enough that I needed to put Plexiglas over it to play, although after several month's storage under pressure it has flattened out considerably. I would have much preferred an unmounted board with larger hexes.