I understand that this question is 10 years old and it already has an answer, but I thought that the answer (if you can call "most likely I think" an answer) was pretty underwhelming.
Obviously, music within visual media (as in, movies, games, TV shows, or accompanying any form of art) is designed to further the feeling a particular scene is supposed to evoke. These pieces are composed for the scenes and not the other way around. In this interview, series director Junichi Masuda describes the process:
"First we bring the necessary scenes to light and fortify what kind of image we want to give off in them, but as the production of the game continues, instances where we say, “I want a tune like this” occur as well, as it was the case with the aforementioned boat scene. So instead of determining how we imagine everything beforehand, we often let the people in charge of the sound actually play the game and then have them produce the tunes."
As far as inspiration, I'd wager that it's impossible to find music that isn't in some capacity inspired or influenced by another piece. It's obviously very hard to know for sure what piece(s) may have inspired pieces from the soundtracks of Pokemon games, but that's not particularly important. As for specific style influence, Junichi Masuda stated in the aforementioned interview that he was influenced by techno and other popular electronic music, and Go Ichinose states that he was influenced by classical music (he specifically states Chopin and Liszt, both Romantic era composers. Classical with a capital C denotes a specific era of music, while lowercase capital refers to all western art music. Thought that distinction was worth making.) and music used in Famicom games. I haven't dug too far into specific influences that the composers have mentioned in interviews, so this is all I can say for certain, but that still leaves us with Ho-Oh's theme sounding nothing like Prelude in D flat major. You're gonna have a hard time directly hearing influence from the composers they mentioned in most pieces, as influence isn't necessarily wanting to sound like another composer, and is often more incorporated into smaller concepts such as how they handle harmony or orchestrate pieces.
Stylistically, there's a LOT happening in the music in Pokemon games, most notably with battle themes, there are huge stylistic crossovers, and I think sometimes easily drawn connections are missed because they incorporate things that are a bit outlandish for the style they're based on. For example, the Lance/Red battle theme is just a rock track with some strings (I'd like to note that some of the stuff the guitar does in the background is pretty crazy, what it does after the into while the strings play the melody is somewhat reminiscent of songs like Metallica's Disposable Heroes). The Ho-Oh battle theme seems to be based on traditional Japanese music with the addition of drums and bass inspired by heavy metal. The Reshiram/Zekrom battle theme is, in my opinion, is somewhat reminiscent of march music (specifically, the rhythms played on the snare drum as well as the flute countermelody, which reminded me of Sousa's Stars and Stripes Forever) and disco/dance music in general (the four on the floor kick drum pattern and the hi-hat pattern, identical to those used in a load of disco and funk tunes, first example that comes to mind is I Will Survive).
Something else notable about soundtrack music is that they often incorporate motifs - notable melodies, rhythms, and the like used across different tracks. The only example I can think of right now is the the similarities between the beginning of the theme used for the battle against Lance and Red in HGSS and the Reshiram/Zekrom battle music, though it would surprise me if there aren't many more. It's also worth noting that both Japanese music and soundtrack music tends (not always) to be a bit more harmonically complex than western popular music, as they both tend to use more complex chord progressions and melodies (more complex melodies often lead to more complex chord progressions and vice versa, not very common to find one without the other). This often contributes to some of the more unique sounds of the music used in Pokemon games.
TD;DR: Soundtracks are designed for certain circumstances, the composers have stated specific influences but will also draw influence from other genres to fulfill the mood that they're trying to create or enhance with a piece.
