I recently bought the Operation Overlord expansion with the Hedgerow hell Battle map.

The Pieces:
The Tokens are sturdy, they are a little better than what you get out of a traditional hex and counter game, but they are smaller than the actual Minis. I like having Japanese pieces because I do not own the pacific expansion and have the chance to play a scenario or two.
The dice are the same ones that come with the Base set.
The Cards are great. This is a good reason to buy the expansion. The cards make overlord easier to play. They are concise and clear; their overlord specific layout makes them a must have for any overlord fan. In addition there are more cards in each of the Overlord decks than in the M'44 base decks. My gaming buddy and I used them for a normal game and loved it. Otherwise, the cards are thicker, which is nice
In addition, there are some reference cards similar to the ones found in the Air Pack for Overlord rules concerning the Pacific Front and the Eastern Front.
The Battle map Its paper but sturdy. I have Paths of Glory and this map seems much better than that one by comparison. But it does lay flat, so Plexiglas is not a must. In addition, the dodge trucks are interesting, but they are SMALL compared to the other minis and are my only let down concerning this expansion. But they do bring another part into the game and the supply rules have potential.
In Play
This expansion coupled with the Battle Map works beautifully. The battle Maps seem well balanced and play tested after one play on both sides. The Cadets of Saumur is my favorite, and it offers lots of options for players. Both battles I fought were close and exciting, and I will definitely play those multiple times. If you get the battle Map, I suggest buying it with the overlord expansion because it is clear that these two go together and you will not be sorry for your choice. This expansion makes overlord smooth and more playable than ever.

Final verdict:
This expansion makes M'44 better. It is not needed if you don't plan on playing overlord, but if you do these two are a must buy. If you really hate the battle maps don't fret; the cards (remember they come with 2 decks) are worth it for the 20 dollar price tag.

In my humble opinion you should not buy just overlord without the battle map because they are closely associated and surprisingly work well together.