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App Engine allows you to have multiple modules within a single application. I'm trying to understand what the benefits of this are over having multiple App Engine projects.
In my situation, I have three components
A back-end component that does all the processing, stores all data, and is accessible with a REST API
A first front-end (e.g., request handlers) component under a first domain name that probably doesn't need its own datastore
A second front-end component under a second domain name that also probably doesn't need its own datastore.
Whether I use multiple modules or multiple apps, the communications between components are done using HTTP requests.
With modules, all the modules use the same datastore and memcache, but with different projects, they will each have their own memcache and datastore. I don't think this matters for me, because only the backend component needs a datastore.
I'm leaning towards using separate applications instead of separate modules because it seems easier to have complete separation.
Is there any reason I should prefer separate applications over modules or vice versa?

The question is somewhat opinion-based but there are many more reasons to use services (as they are now known) over separate projects.
You cite the main reason in your question: shared back-end services. Although you don't think that matters as they probably don't need Datastore, I would rather assume they may need them in the future than not (and then have to integrate via your other application's HTTP interface instead of direct Datastore RPC).
By using different services in the the same project, you benefit from simpler access to other Cloud Platform services (e.g. BigQuery) through things like service accounts.
You also get things like service discovery through the Modules Service. If you were to deploy as separate projects, App Engine doesn't know your projects from mine.
By using separate projects, you get pretty much the same separation as using services, but forego the benefits above.
Some people might want to use a separate project to benefit from an extra 28 free instance hours, but that wouldn't be a great long term design goal for my liking.