How important is an (Honors) undergraduate thesis to graduate school admissions?
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.