In general: When 4Kids started off, their BGM was alright, but near the end it was horrible. TPCI started off horribly and is now alright. I think the 4Kids BGM is more dull and TPCI do seem to be remixing a few of their tracks in an effort to improve them, so I think I'll pick TPCI.
What I have noticed that I thought was a little funny though, while I was watching the first series of Yu-Gi-Oh (the 4Kids dub), I would notice a few seconds here and there that sounded exactly like some of the 4Kids tracks from Pokemon. I noticed one in particular that sounded like a part of the track "Three on Three" from the first Pokemon movie. Of course, the tune changed again after a few seconds, but I found it funny all the same.
What I have noticed that I thought was a little funny though, while I was watching the first series of Yu-Gi-Oh (the 4Kids dub), I would notice a few seconds here and there that sounded exactly like some of the 4Kids tracks from Pokemon. I noticed one in particular that sounded like a part of the track "Three on Three" from the first Pokemon movie. Of course, the tune changed again after a few seconds, but I found it funny all the same.