Of course anyone would want to be able to do both! (Speak/understand, and read/write.) And the best way to learn any language thoroughly is to learn with a nice balance on both.
But I'm assuming the question is hypothetical; along the lines of, "If a miracle could happen and you could wake up in the morning with suddenly a fluency in one aspect of the language, which would you rather it was?"
I'd choose speaking/understanding. From my viewpoint, the purpose of language is for communication, and communication through speaking is the most widely used. ^^ Additionally, as someone pointed out, if you can speak the language quite fluently, it's easier to get a native speaker to help you with the reading and writing.
As for how I am trying to learn . . . I just went to a regular college evening class, at level 1 only (nvq level 1), and the tutor was a native Japanese speaker. We learned speaking first, and had some written notes in romaji for the first few lessons (because you need some way of remembering!), then we learned hiragana/katakana (well, I'm slightly biased because I knew them already ^^), and during the course we learned the speaking and the reading/writing in kana simultaneously. Some people were slow at learning the kana, though...
I think that learning the speaking and the writing tend to naturally work side by side when learning another language, because you need to have some kind of memory-jogger to remind you of the sounds of what you've learnt! If you can't write it down, it's much harder to hold the sound in your memory! (I find that writing something down helps greatly to fix it in my memory.
)
Of course, if you are living in Japan and hear the language a lot, you probably wouldn't need to write it down nearly so much in order to remember.
I'm just thinking of people like me, learning by classes and self-study. ><
Also, I find that learning certain things in speech first, makes learning kanji a lot easier. Because of the different readings... if you were to just attempt to learn the readings, it can be a little confusing. But if you already know the words/phrases in which they're used, it all falls into place when you see the kanji! (For example, 'ima' and 'ko'... they don't sound related, but once you have learned, 'ima' as 'now', and 'kotoshi' as 'this year', it makes perfect sense and you can't forget those readings!
) (sorry, I can't type kanji on this machine >< -_-)