As @ʞɹɐzǝɹ and @seijitsu mentioned in the comments, these designs appear to be based on birds. Specifically, the long neck and football-shaped body look like a crane or goose.
The red-crowned crane has a significant place in Japanese and Chinese culture. It figures in the fairy tale Tsuru no Ongaeshi. As txteclipse mentioned in the comments, Japan Airlines even uses the red-crowned crane as its logo; the Wikipedia article says this symbol was chosen by an American branding expert due to the positive image of the crane in Japanese culture and mythology. Given that, it makes sense that Japanese artists would think of using the crane as a basis for imaginary creatures or flying vehicles.
The crane-like design is also unusual in real world aircraft. As you can see from the first image of the goose, the goose's and crane's wings angle forwards; this is replicated in the OP's first image of the Gekko from Eureka 7. Real-world aircraft tend to have a more straight, cylindrical body and wings which angle backwards:
These differences give aircraft based on the crane design a unique, fantastical appearance.
I couldn't track down any species of crane or goose which has tufted "ears" like the Gekko or Latios. Some geese do have tufted feathers, but they seem to be always on the back of the head. However, some bird species, such as the the great horned owl and the juvenile of the house finch, do have such tufted "ear" feathers:
When it comes to designing a fictional creature or aircraft, a design based on the crane's head is a little bit boring to look at. The tufted head feathers also come from real-life birds, but they add visual interest to the head area, without seeming too ridiculous or over-the-top like the head adornments of certain bird species.
