How important is an (Honors) undergraduate thesis to graduate school admissions? I'm an undergraduate Honors student in a STEM major, and in the upcoming years I will have the option to complete an Honors thesis in my field, either as a research/data analysis or a literature review sort of thing. Because of other circumstances I can graduate "with Honors" with or without it, so it would purely be adding to my major, not so much my overall graduation status. 

Either way I will have some volunteer experience in labs in my field, and a decent GPA, etc. Would an undergraduate thesis in my field greatly help my graduate program applications? Does it matter if the thesis is based on original research or literature review?
The part of an undergraduate thesis that helps you with graduate admissions is that it is a form of research experience. It's not so much the finished product, the thesis, but the process of getting there and putting the work in. Even if it isn't complete before your applications are due, just that you are working towards a thesis is useful if it will get you into a lab and learn among other people doing research.

In my personal opinion, a literature review isn't nearly as useful for building the skills that make you a good grad school applicant, it's a lot more like the rest of the (upper-level) coursework you do as an undergraduate.