They are certainly different series.
However the 'prestige' and general usefulness of any given Handbook volume doesn't depend a whole lot on the publisher. It depends much more on the editor(s) and the other authors who will write chapters, and whether the coverage will be useful to people who work in the field and those who might wish to enter it. To the extent that 'prestige' is important, it's the prestige of the editors and contributors that will draw people to the volume, but they will only use it, learn from it, and cite it (and you) if they find it helpful.
You should also think how useful it will be to you, at this moment in your career, to devote time to writing a survey on the area you have been asked to write about. Is the moment ripe to write this survey? i.e. are there lots of papers that could usefully be brought to people's attention in ways that they now are not? To write a good chapter is a time consuming and demanding task, but afterwards you will probably have a command of the literature that you don't have now, and if your chapter is useful to people, it may also play a role in guiding people towards topics and papers that you believe are important and worth attention...
