HOD literally had the main artist of Castlevania ( the creators wife who was interviewed in "PLAY magazine" ) given more options. She is resposible for the look of Castlevania from it started and especially the PSX game.
HOD actually have some hidden play modes via various password usages.
For me it was my First official physical play of Castlevania outside of emulators. Buying this game and playing it on a GBASP was amazing.
In comparison to the PSX game "Syphony of the Night" HOD is a cake-walk ( or drinking barely water ). But the whole purpose of the game is to enjoy it as much as possible, while being a Gameboy game. The game is literally a play-by-play of the PSX game from a different point of time. Automatically from the get go you are in the shoes of the PSX game.
Circle of the Moon is literally like the first SNES game. It is there to be a GBA game that took advantage of being a GBA game. HOD has tons of visual improvement in terms of "being more realistic in art movement", where COM is more or less a traditional 2d pixel-art game. You will even see the 3d-clock-tower as you march towards Dracula.
You want a fast paced game that looks great then play HOD. The problem with HOD is replaying it, because it feels like work. Also the enemies are much more appealing. Like what the fairy from "Berserk" looks like. COM is more like if Simon was the main character and it was modern times.
You want a game that is sluggish, challenging, and your characters are ripped out from Sherlock Holmes then play COD. Also the enemies are kinda goofy and obviously ripped from other games. In fact this game is more or less akin to the N64 game and it's enemies structure. Insane, and over-powered, and completely not logical.
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Here is the problem with every Castlevania after HOD. It is the sales of the game itself. With AOS
( a present day, modern, mature but stil youthful ) you have this idea of revival but it becomes more about the cards, and attempts to focus on the beauty of white, while being more pixel-art rather then
GBA ( Vector surreal better looking ) art.
Konami also had a change in power structure ( which we know all too well ). The flat fact the NDS was not being purchased in high numbers, and the art style shifted towards being Anime ( unlike HOD artwork which was fine-arts ). NDS games is like if somebody took a step back to the Mega-Drive ( Genesis ) era of games. Imagine an over-powered Genesis system with the 32X power and shading and color blending and usage of the SNES.
NDS games are completely alien to me. I find myself wanting to checkout the Wii, MD, or other missed CV titles.
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I believe the direction of COM contrasted with HOD ( Wife of the creator of Castlevania series ) involvement.