In many ways, I consider Drakengard 2 to be a much better game than the original Drakengard. It has a few severe flaws, but for the most part its story and gameplay are a significant improvement over the original game.
Gameplay in Drakengard 2 is organized in an identical manner to the previous game. There are ground missions in which you fight large numbers of soldiers with weapons, magic, and dragonfire, and aerial missions that feature dogfighting between your dragon and aerial foes. The terrain is more varied (and far less flat) in the ground missions this time around, aerial missions are a bit more complex, and there are a few minor nods to blurring the lines between the stage types, but the basics of gameplay are the same. However, there are a number of significant changes that make the whole game feel very different.
One major change in the game is that there are no more red-armored soldiers who are immune to dragonfire. Every enemy can be at least harmed using attacks from your dragon. However, the same role is filled by the large monsters such as ogres, minotaurs, and behemoths, who will counter-attack and knock you off your dragon if you try to defeat them with dragonfire. Unlike the red-armored soldiers, though, these enemies can be defeated quickly and tend to be an interesting fight, so it is never tedious (I recall always using physical attacks to defeat them, so I can't remember whether they are immune to magic or not). Also, the role of "enemies who can not be hurt by magic" that was filled by red-armored soldiers has been given to undead soldiers this time around, who mostly only appear in indoors missions where you can't use your dragon. Also, archers and the effect of being knocked off of your dragon when consecutively attacked remain from the last game, though archers tend to appear in smaller, widely distributed groups in this game.
As a whole, the game does more to restrict your use of the dragon through design of the stage map and artificial restrictions on the dragon's availability than through certain enemy types. It has more dynamic stage locations like small tunnels the dragon can't access and narrow passes filled with archers and mages, which actually serves to keep things very interesting when completing stages because the situation can change so much more in the middle of a mission than in the previous game, and the decision about whether to use your dragon or not is more complex. Even the experience system has been changed to make you think more carefully about using your dragon or not, because unlike in the previous game, killing enemies with the dragon will not build up the hitpoints or other stats of the other characters.
While using stage design to get rid of the need of red-armored soldiers is a good thing, it seems to come at a pretty severe cost. Namely, Drakengard 2 has very few stages like the dominant stage type of the previous game: large-scale battles against hundreds of soldiers where you can rain down dragonfire to level an army. Most stages of a similar type tend to have much fewer enemies than similar stages would have had in the previous game, and in the one stage that actually has a large number of foes you can fight on dragon-back, you are fighting in a closed area and the objective is merely to kill a minor fraction of the enemies present, rather than use the old Drakengard system of having both targets you must kill to complete objectives and large numbers of enemies you can kill for fun. Finally, no mission in Drakengard 2 compares to the early missions of the first game, where there are countless enemies far off the normal mission path. Instead, the game tends to leave areas you don't need to visit fairly empty. The end result is that the missions are a bit too focused, and you ever really have a good opportunity to just fight a lot of enemies, which is part of the point of this genre of game.
That being said, the general improvements to the game, such as better controls, the adjustment to the ally characters to be equal in importance to the hero (they are no longer cheap super-weapons at all), creating different enemy types who are strong or vulnerable to particular characters, the addition of flashy Dragon Overdrive attacks, and various other changes, make ground missions a lot of fun.
Aerial missions in Drakengard 2 are very similar to the previous game, except now they feel even less important to the main game. In Drakengard 2, most boss battles are now ground missions, so one of the ways aerial missions were given importance in the last game has been limited. In fact, one of the boss battles in which you use your dragon to fight an opponent is technically a ground mission (which just highlights the fact that the game would have been better if there was more room to transition between proper ground and aerial missions). Also, I don't like the change to the dragon's magic in this game. The "breath spheres" are an awkward mechanic, and their importance and dependance on using direct attacks makes homing shots too much of a poor choice. I think it would have been better if they simply created an aerial version of the Dragon Overdrive system.
I still have a lot more to say about the two Drakengard games, but the kind of detailed analysis I want to do would take up too much space in this post, so I will save it for another day. Both games have very convoluted characters and plot/gameplay structures, after all.