I played many hours and many campaigns in HoI ages ago and enjoyed it. I hoped to enjoy DH: HoIG as well, but really couldn't.
The advantage of HoI was that you could do alternate history, changing the course of events, etc. DH pretty much forces you into a very pre-determined course. I tried playing as Yugoslavia, 1936 and in spite of beefing up an army, fortifying borders, doing my best to stay out of the coming war, having excellent relations with Germany, Italy, etc, come 1941, scripted ultimatum by Germany, your choices are "become a puppet" - game over or "be invaded" - game over.
Tried playing as the Soviets, HoI gave you a choice "do Stalin's purges, lose a third of your generals" or "don't do purges, see your dissent skyrocket". DH gives you no choice, purges just happen, you lose a third of your generals AND your dissent skyrockets (weird actually, since the purges had a rather opposite effect, putting everyone in line with the dictator's commands).
So, basically the player has very little freedom of action, outside of the developers vision of how a scenario should play out. This, to me, defeats the purpose of a sandbox grand strategy game...
Bias or unbalance. I got a distinct feeling the game was very pro-Germany biased. I tried a 1933 Soviet scenario and tried to play a "nice Stalin" one that helps and liberates, rather than opresses. Got involved in the Spanish civil war, took over the troops, helped Republicans get a clean win. And the thanks for my effort? Minimal relations increase, no alliance, a puny 1% dissent decrease (but for changing a minister I ger a 2% dessent increase), no military experience, basically nothing.
Got involved with the Chinese in fighting off the Japanese invasion, by inviting Commie China into an alliance. Automatically Nationalist China also becomes an ally. I soundly beat the Japs, annex Chinese territory which automatically transfers to (should at least ask me which China I wanna give it to) Nationalist China. Japan asks for peace giving all Chinese territory back and Korea and Pacific islands too. I accept, Nationalist China becomes huge, but both Chinas immediately break off the alliance with me and go into negative relations. I immediately liberate Korea, but my belligerence goes up. I get no option to liberate Pacific islands and am forced to give them to Korea if I don't want rebellions.
I don't give any ultimatums or invade Finland, but they still hate my guts and try to assasinate my ministers. And French and British keep trying to assasinate my ministers. I don't accept Hitler's pact to divide Poland, but he still invades it, just instead of getting half of it, he gets all of it. My belligerence is still in its 70s just for helping liberate China without keeping a single province to myself, while German one after invading the entire Europe is in its 50s.
I fortify my western border with bunkers, behind rivers, upgrade all my troops to latest level, research nothing but land tactics, beefing up my ground forces to latest standard of warfare, got 1941 tanks in 1939, good and skilled generals in command. No good. When the Nazi decides to invade, he's got at least 100 divisions more than me and in spite having lower organisational rating, still cuts through my lines like a hot knife through butter.
Oh, and Lend-Lease. US sent over 20,000 tanks and airplanes to the Soviets. What does DH game give me? Not a single tank or plane, but 50 units of roads instead.
Airforce is entirely useless. When the Nazi invades, I got complete air dominance (his planes are likely over Britain). I pound an advancing column with my entire airforce of 4 Tactical bomber groups, 4 close-air-support groups and 12 fighter squadrons all in their latest 1941 upgrades. And all I kill is 400 enemy men out of 100,000, practically don't even scratch them. No organisational disruption. No advancement slow down. Nothing. All money spent on (expensive) airforce is completely wasted.
Diplomacy. Pretty useless. Any alliances, non-aggression pacts, demanding territory, outside of scripted ones are practically impossible to achieve.
Intelligence. Pretty useless. Chances for any actions are so low and so expensive, that the money is utterly wasted on them and coups, sabotages, etc are practically impossible or if they happen they're definitely not worth the money in the minimal effect they have.
I suppose the only way to have a chance is to invest everything in a thousand infantry divisions with artillery attachments and all the money into research boosts so you get blueprints for stuff every time. All the other features are useless and a waste of time. I'm a stubborn person, so I tried same scenarios several times, trying to make some optimal decisions to enable me to gain the upper hand, but the game just keeps blocking any progress I make by its punishing mechanics, limiting diplomacy and disruptive random events. Maybe I should just play as Germany and steamroll everyone.
Verdict: Forced. Unbalanced. Biased. Frustrating. Unrewarding. Punishing. Irrational.