Why I prefer TVXQ (Yunho and Changmin)'s music to JYJ's is for the most part related to their voices and how they fit and mould (or don't) together.
While many a Cassiopea will probably think this analysis expresses personal bias, I honestly assure you that I have tried to be objective as possible. Hence my explanation in detail as to why I have this preference. No one needs to agree with me of course but if this entry helps give people insight into the beauty of TVXQ's music the way I see it, then great.
Pre-lawsuit / DBSK as 5 era:
Back when I first started listening to DBSK, I confused some of the member's voices. After it happened repeatedly (and with the same members), I decided to seriously try and figure out how and why it happened. Eventually I came up with a line regarding the similarity of their voices regarding texture. Naturally, members with more similar voices have more ease and better success at harmonizing.
To describe the voice similarity in one way, we can use pairings:
Yoochun and Yunho
Yunho and Changmin
Changmin and Junsu
Junsu and Jaejoong
A better description I think is however the line of overlapping (similarity) I came up with, looking like this:
Yoochun -> Yunho -> Changmin -> Junsu -> Jaejoong
As the group had an uneven number of members, one member was always left somehow out of place in the songs that relied on voice compatiblity and similarity instead of contrast. Of course said member had to be on one of the far ends of the line aka Yoochun or Jaejoong whose voices have the biggest difference.
By DBSK5, one song, and my personal favorite, stood out as a great example of this 'voices blending together almost effortlessly' and that is Darkness Eyes.
I provide a link to the song because it would help fans understand this analysis even better with an example.
In both verses and chorus fans can hear for themselves how members have been paired off as more compatible voice wise and who is (albeit not obviously) left out of the equasion.
The odd one out in this song is Yoochun, who for the most part is stuck repeating "Darkness on my eyes" in the chorus in order to further strengthen the mood of the song. His voice fits the meaning behind the lyrics perfectly, but doesn't make him any less left out regarding voice fitting with the rest of the members. Even the one verse he sings in the beginning of the song (following Yunho's start) seems slightly out of place when the song is taken as a whole.
As fans can hear, the pairs whose voices mold together are determined as Yunho and Changmin (coversing first verse and second chorus) and Junsu and Jaejoong (covering first chorus and second verse) in order.
I will admit that the first few times I heard this song, I had trouble distinguishing Yunho and Changmin and hence found them to be the members whose voices blend together best, almost as though it's one voice. Junsu and Jaejoong's blending was more apparent to me in Rising Sun, but more on that some other time.
Skip three years into the future and we have TVXQ as a duo and JYJ as a trio. I think both units are doing very well separately and am not desperately waiting for the day they are together as five. However, once having determined my line of similarity, I now have a better understanding of why I prefer TVXQ's music to JYJ's (American debut aside).
TVXQ as a duo has little problem harmonizing as it is Yunho and Changmin, whose voices overlap in a way and blend together due to their texture's similarity. I am no expert so I am probably not using the proper terms but upon listening to songs like 'I Think You Know' or 'Before U Go' or even 'Our Game', fans can hear for themselves and see what I mean. It is exactly that beautiful compatibility and moulding of Yunho and Changmin's voices that steals my heart away again and again with each song they make.
On the other hand JYJ have two members whose voices fit incredibly well - Jaejoong and Junsu and one member who is left out - Yoochun.
Yoochun -> Yunho -> Changmin -> Junsu -> Jaejoong
Between Junsu and Yoochun there are two voices missing. As a professional, he can harmonize with Jaejoong and Junsu, but that two-person gap between him and them is still incredibly difficult to fill in. That is how, in songs relying on harmonizing and voice compatibility he ends up mostly rapping - see 'Mission' or barely singing - see 'I.D.S'. Then there are songs relying on contrast where he covers the verses single handedly, which seems to be JYJ's best bet at this time - see 'Empty'. Of course, there are other examples of these as well, which I am sure many JYJ fans can think of.
That being said, I love both TVXQ and JYJ's music. I know all five members' talent doesn't go to waste.
Perhaps I have missed something, and if I remember it, I will edit this post later on. Please, do keep in mind that I have no education in music and trust only my ears when I make observations. I have no serious claims to being right, although I have put effort into being as fair and objective as possible.
Comments are welcome as long as they are not too harsh :P