I'm a fan of strategic-level World War II games, and I've played any number, starting with the old World War II from SPI.
Like Strategic Command: European Theater, Commander - Europe at War uses a hex map, is turn-based, and is limited to the European theater. In general, I tend to think that hex-based wargames are humorous--we adopted hexes for boardgames because they provide a better tessellation of territory than a square grid, but computers are quite capable of calculating true distances trivially, so to my mind, the use of hexes in digital games has always been a technologically unnecessary homage to an earlier non-digital style. (Of course, one might say the same of provinces.)
But never mind. Commander has what I'd consider the right level of detail. What do I mean by that? Well, in say, Gary Grigsby's World at War, there are only two French provinces facing the German frontier, and any successful 1940 attack on the French goes through the Low Countries, meaning that there's no apparent distinction between the Schlieffen Plan and an attack through the Ardennes; in Commander, there are enough hexes that you can see the difference between an attack through the Ardennes forest and one via the Belgian coastal plain. On the other side of the equation, some games, like Hearts of Iron II are so fine-grained that you feel like you're micromanaging your forces, and playing the whole war takes forever; Commander is sufficiently granular that you don't feel tied up in slow, petty little force deployments. It's a happy median.
The production system is reasonable, if in some ways, flawed. You have three constraints: production capacity, manpower, and oil. Production capacity is directly tied to cities (which is somewhat ahistorical--e.g., the conquest of France certainly reduced Allied production capacity, but did not add to Germany's to anything like the same degree). Manpower is based solely on the nation. Oil doesn't affect production directly, but all units bar leg infantry consume oil with each action, which in the late game is a dire constraint on the Axis (but not on the Allies, nor on Russia, unless the Caucasus should fall).
When building units, some do take longer in Commander than others -- but the spread of construction times is far smaller than historical reality: leg infantry takes one turn (week) to construct, and battleships six; in reality, laying down and building a battleship takes many months, even given the urgency of wartime. World at War handles this better.
Reasonably, Commander has the concept of 'national effort;' e.g., in 1940, the Soviet Union and the US are devoting only a fraction of their national productive capacity to military construction, and increase it over time. However, the Germans are producing to their limit from the inception, which is historically wrong; not until late 1942 did the Germans decide to mobilize entirely for war. (The Nazis had an ideological attachment to the idea that women should remain at home, preferring to keep men in the factories rather than drafting them, supplementing them as necessary with slave labor from the conquered territories.) However, given that the cities in Germany provide only a small production basis, and the game gives the Germans most of the productive capacity of conquered cities later in the game, this is probably necessary to make the production levels balance out to something reasonable--pointing up the flaw of the city-based production model, of course.
Many other games (including World at War) tie tech development directly to production--that is, you use production points to increase your tech level. To my mind, this is fundamentally flawed--except in the case of the Manhattan Project, few technical advances in the war depended on the use of productive capacity. Rather, they were limited by available technical talent and, e.g., scientists devoted to cracking codes or building better radar inherently weren't available to making better airplanes or building an A-bomb. In other words, available technical talent was certainly a constraint, but a different constraint from the size of your industrial base. I've yet to see a game that acknowledges this.
Commander is a little different; you have to use production points to build science teams, but once you've done so, you can allocate them among different tech development priorities independently. Also, new tech, when developed, doesn't automatically devolve to your units (as in World at War); instead, you must spend tech points (as in HoI II) to upgrade your units, which is reasonable.
Commander does an excellent job simulating the fluidity of blitzkrieg warfare--indeed, far better than the province-based games, because the granularity of the hexes allow you to better represent penetration and encirclement. In fact, this is where the game excels, at least for me; particularly in East Front battles, you get a far better sense of the nature of mechanized warfare than you do in either HoI II or World at War, where things feel much more like a slugfest with armor as your stormtroops.
Seemingly (in my limited number of plays), both the US and the Soviet Union will intervene on the Allied side by end 41, regardless of what the Axis does; while this is probably essential to provide a balanced game, it's also (from my perspective) annoying. While Japan is off-map, and presumably attacks in December 41, I do want the option (as Germany) to avoid Hitler's mistake of declaring war on the US--and let Roosevelt try to get a declaration of war on us through a reluctant Congress that would rather crush the perfidious Japanese first. Similarly, despite many warnings from both his own commanders and the Western Allies, Stalin seemed oblivious to the potential of German attack in 41 until Barbarossa was well under way; if Hitler had wanted to string the Russians along another year or even longer, it's quite possible he could have done so.
I like WWII games in which Seelöwe (the invasion of Britain) is possible--admittedly in reality it was fairly unlikely, but with enough commitment and minor differences in strategy, perhaps it would have been feasible. In Commander, however, it's almost too easy (at least starting in the 40 scenario); when France falls, there will be only a handful of corps in the UK (which is realistic). However, any unit next to a port can turn into a transport, move to the UK and, on the next turn (allowing a turn of attacks by British naval and air), land. They will then be out of supply--unless a German naval unit is on a coast traceable to the invading unit.
So all you do, basically, is move the one German battleship unit into the Thames estuary to provide supply, land a half-dozen German corps, and Bob's your uncle. This is, frankly, absurd; in reality, the Grand Fleet would steam out of Scapa Flow, blow the tiny German surface fleet to kingdom come, and savage the eclectic collection of merchant ships and destroyers the Germans were relying on to transport troops to England. Germany's only hope of pulling off an invasion of Britain relied on first achieving air supremacy over the Channel (and therefore the ability to destroy or at least badly damage the British fleet if it intervened)--which is what the Battle of Britain, which the Germans lost badly, was about: an attempt to achieve air superiority.
Oil becomes a major constraint on Axis action by the mid-game. They're critically dependent on the Ploesti oil fields in Romania (historically true); every time you use a naval or air unit or armor, 3 oil units are expended, and 1 for mechanized inf. By mid-1942, this means you've essentially run out of oil, and are limited to one minor offensive per turn. Since Soviet production ramps up much more slowly than historically (even in 1941, the Russians were producing more tanks per month than the Germans by a considerable margin, and as their battlefield losses declined, the preponderance of forces shifted with remarkable rapidity), the oil constraint is about the only thing that shifts the control of the offensive to the Soviet side. So okay, it suffices to produce an historical shift, but it also pretty much forces the Axis into a drive for the Caucasus--which, of course, Hitler insisted on, but the rest of OKW fought against, in favor of a renewed drive for the conquest of Moscow. Also, there's no simulation of the successful German effort to build factories inside the Reich to transform coal into petroleum, which helped immeasurably during the war (until those factories were destroyed by the Allied bombing campaign in 1944).
Still, all of this is criticism on the margin. In total, this is a comprehensive, thoughtful simulation of the European conflict, at what I'd consider the "right" level of granularity--a level capable of showing important strategic considerations without bogging you down in the petty detail of HoI II. The production model is susceptible to criticism, but is no worse, and in some ways better, than those of the other games.
For those of you interested in strategic-level WWII games, I'd say: play this thing.
N.B.: The game's been out for a couple of years, but we don't normally link to anything unless there's at least a demo you can download online, and they've only recently released a demo.