Egao no Daika

The two series have a similar world, a similar set-up for conflict, characters with similar traits and circumstances and are largely character-driven. In both stories, two sides (nations in EnD, an empire vs. a union of nations in AZ) are fighting a war over resources. One side can't feed its people due to environmental circumstances of the land they inhabit. One side is technologically superior to the other due to a mysterious energy source available only to them. Thus they have more powerful mechs while the other side has strength in numbers. There's an idealistic, peace-loving princess leading one of the waring nations, being more of a figurehead than an actual ruler. Said nation also has strong chivalric values that the other lacks. At the heart of both series are its dual protagonists. There's one on each side of the war, giving us insight into both sides' motivations, reasons and methods for the war. Both protagonists are sympathetic. One of them is emotionally upfront while the other doesn't show their emotions, though there are subtle (or not so subtle, depending on the series) hints to what they're feeling.  read more 

the same situation where it was set in some setting where it experiences turbulent times and it involves a princess and a very special girl, to put chaos at ease.  

Both series have heavy focus on the grunts in war, with mass produced mecha used as replacements for traditional infantry. Stella's characterization is reminiscent of Chirico's, and the episodes where she is the lead are the ones that will be most enjoyable if you liked VOTOMS. 

Both sides are neither good nor bad, but are both at war to stop war. Both shows tend to shift between the perspectives of each sides in order to depict the "no true bad guy" theme as well attempting to give characterization to the involved cast members. Both shows also tend to be heavy with constant deaths for shock value and consequential events of war. LOGTH, though, tends to showcase the similar themes significantly better. Yuki and Stella, the two main lead heroines, are sorta equivalent to Reinhard and Yang, respectively, though with very notable, obvious differences.  

On these two shows they explore a lot the worst of the war, about the political envolvement that the people from the two sides don't know and still dying because this. If you like mecha, good fights, amazing ost and a lot of feeeeels , will be perfect to you. 

Futuristic setting. War between two nations that has been raging for generations. Barely anyone still remembers what even started the fighting. There is no clear distinction between which side is good and which is evil.