Here's the Google face-off:
Wiktionary seems to agree - their definition of a Bioinformaticist is: a Bioinformatician.
My actual job title is bioinformatician, but weirdly enough the term that comes to my mind first is bioinformaticist. I believe the latter is earlier in usage, but the former has become more common.
It still occasionally happens that if you tell someone who has no idea about science whatsover that you are a physicist, they will accord great respect and deference and often ask you about their medical problem. Once they find out you're just a "scientist" their deference almost disappears and is replaced with either confusion or slight disdain.
This varies with culture, I'm sure. Go to any hospital nuclear medicine department, and see if you can spot any medical physicists wearing white lab coats.
Something similar may be involved in the semantics of -icist vs. -ician, possibly having to do with the tools vs. the tasks of the trade. Engineers and computists(!) obviously identify with the tool-making, and almost everyone accords them respect. However, more and more, I think that those who can take a biological research [data] topic and work through its solution with whatever tools work well, are becoming the thought leaders.
Maybe we say "physicist" because "physician" often refers to medical doctors? Which might bring it down to what most people use... Personally, I mostly hear people using bioinformatician.