In general I prefer dubbed because the songs etc are better and you can relate the character to their voice more, however most of the time subbed has much better voice acting so it's a pretty hard choice. :p Really it depends on the show most of the time, but in general I prefer listening to English.
Wait...did you seriously just say that you prefer dubbed songs over the originals? Seriously? That's the first time I think I've heard anyone say that...ever. Not that I have anything wrong with this, I'm just very interested in the fact that you say it. Do you have any anime in mind where that's the case? I mean, I can understand songs like Freckles (Ruroni Kenshin's OP), because they sound almost the same in terms of vocals (and the English version is redone, so the intro to the song is cleaner)
(Seriously, it's hard to believe that they're different people)
Some more examples would be Dragon Ball and Yu Yu Hakusho, both of which actually really care about the songs they're singing, and get quality singers to do the job (often trying to match the voice or tone of the original singer), that way it will still pull in in viewers. This isn't a common practice, mainly because originally English openings were created to make the anime more localized and less Japanese.
As you can see, authenticity was key, and they tried to match the original songs as best they could, most likely because that was the way the original composers meant for them to be sung.
Then, you have shows like Digimon and One Piece. All of these shows suffered from certain producers wanting them to seem little Japanese as possible, and for this reason they changes their openings entirely, often using lower grade and weakly put together openings, often using scenes from the show (or rearranged pieces of the original opening) and adding sound effects to the song (though, this wasn't uncommon among the original songs), as well as going off of some type of fad as the basis for their song (Rap was often used, mainly since it was used in cartoons, and it worked- in cartoons, that is, not anime).
They're goals, however, weren't to create a good translation or even a good substitute, but rather, to create a catchy opening that people would remember, especially children, even if the song itself wasn't that good.
Then, there were shows like Pokemon, Dragon Ball Z, and Yu-Gi-Oh! which did the same thing, except they took care in what they were doing rather than simply what they were trying to do. While the former shows indeed had openings that were catchy, not nearly as much care and effort were put into their creation than these, and even if the audience didn't care about the quality of the shows, the songs themselves ingrained themselves into the memories of their viewers. It's hard to find someone who watched any of these shows as a child who can't remember how their themes go.
Even still, they couldn't resist showcasing action-packed moments rather than going for the tone of their originals, not that they went to their discredit.
And yes, I did use your post as an excuse to take a look at dubbed openings. Though I still am interested in the ones you have in mind