As @r0bby points out “OpenMRS” and “LibreHealth” are communities, not specific products. But to answer your question (of course this is just my opinion, as an architect on the Bahmni team, and a cofounder of OpenMRS):
Bahmni is an EMR and Hospital System, built on top of OpenMRS, OpenERP/Odoo, OpenELIS, and dcm4chee (though all but OpenMRS are optional). Bahmni gives you a “typical facility” system out the box, without needing to do any custom development, and it’s backed by a large, professional, product team. The target implementation would be a low-resource hospital or clinic who wants an electronic system to manage their patient EMR, as well as other hospital workflows (especially if their main concern is to use the system, and not to get directly involved in software development).
OpenMRS Platform is a platform for building patient-centered medical record applications, providing Java, REST, and FHIR APIs. If you want to build your own application, and do heavy development work, this is a great place to start. (For example Buendia, the Google-MSF Ebola tablet application was built on this.) You can also assemble a complete EMR application without writing any code from the OpenMRS Platform plus various plugin modules. This has worked well for retrospective data entry use cases, though it’s hard to achieve a full point-of-care workflow this way.
OpenMRS Reference Application is a point-of-care application built on top of the OpenMRS Platform. It is not as feature-complete as Bahmni, so I would recommend Bahmni over this for most implementers. (It is also has a bunch of extensible building blocks if you do want to customize; I was the tech lead of a ThoughtWorks/Save the Children project and we quickly built an Ebola tablet system on top of this.)
I can’t personally speak to OpenEMR; from spending 2 minutes on their web demo it looks closer to a US/European hospital EHR than any of the others.
LibreHealth Toolkit is a fork of the openmrs-core codebase. Based on this other thread the intention is to make fundamental changes, and not preserve backwards-compatibility. so my advice to an implementer would be to hold off on this and see how that aspiration plays out.