This vote is so difficult it's painful! In the end, I've got to go with Growing of My Heart. It's got the driving beat, great music, awesome visuals and superb timing. I can't think of a better way to get psyched up to see a brand new Conan.
What's interesting is that Kimi to Yakusoku Shita is used for arguably the greatest episode ever (345) and the multiple cases that lead up to it and Growing of My Heart is used for...the most boring manga case ever, Agasa's Love, an AO Yusaku/Yukiko case and AOs so bad they should have been aired recently. And yet Growing of My Heart seems more...climatic I guess.
Both songs are great, but Kimi to gets my vote because I am in love with the sequence, whereas I could take or leave GOMH's sequence.
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Kimi to Yakusoku Shita Yasashii Ano Basho Made. Besides being used as the opening to one of my favorite cases, and having a awesome sequence, when I first heard it, I became quite addicted to the song. Where as Growing of My Heart was okay, but it didn't have the same rushing feeling that Kimi had.