A computer scientist can manipulate any file type commonly seen in bioinformatics, but may not understand what the underlying biological questions are. A biologist can ask the questions, but as we see on a daily basis here on Biostars, may not have the training to run or debug a program raising an error, leaving little to go on to provide support. So, what is more important for a Bioinformatician? In my personal experience, it is a hybrid of the two, as the name implies. We build tools to analyze, sort, and report data ranging from simple tests to complex statistical analyses. However, we shouldn't be just technicians for bench scientists, often to whom we must relay results from a biological context, and not the technical aspects within a piece of code. Alternatively, to my experience, I've met many bioinformaticians who do not have a biology background, who focus more on the computer science. This post is intended to discuss the opinions of Biostars users in regards to the importance of biology vs informatics, for a Bioinformatician.
As you already said:
It could vary from day to day. Specially if you do this as a "service" (either for a fee or via some other support mechanism).