I usually write my dreams down in a notebook next to my bed, with varying degrees of detail. Normally it's just a few notes that wouldn't really make sense to anyone else, but I can remember stuff from them. It is hard to move details around with the real DJ, so things in mine often end up written in a strange order. ("Oh, I just remembered, in the part before, this also happened...") I find the notebook easier and faster to write in when I've just woken up.

I recently started writing in my DJ here, though, and I have to say I like having tags and categories. That way you can see what appears a lot in your dreams, see dreams about a particular subject, reread memorable or lucid dreams, etc. much more easily. Also when I type them up to post here, I end up writing in a lot more logical order, and with proper sentences and paragraphs and all the details and stuff, which I think is good lol.

So basically I don't think it matters too much, and there are advantages to both.