Hi Jennifer,
Welcome to Moodle.org forums!
I prefer getting learners to submit essays/texts as online assignments. That way, I can use the built in tools for marking and commenting and also insert links to other resources and modules whenever necessary. I wrote an article about using the Glossary module and text filters for providing feedback for foreign/second language learners: http://blog.matbury.com/2012/03/01/using-moodle-for-written-corrective-feedback/
As far as using mobile devices for text input... well, some learner may have problems with that. I've noticed that compared to their submissions from PCs and laptops, when the same learners use tablets (checking the server logs for their OS) their submissions are shorter, have more typos and errors, and tend not to be proof-read either. It could be because they may be in a disctracting environment or because of the virtual keyboards. I don't know.
Learners with iPads and iPhones had the worst time. We couldn't find any way of uploading photos, audio or video. The only way is for them to use the computer the device is synced with (you're only allowed one), transfer it to that and then upload it. It slows projects down to a crawl and is a real pain. Didn't have the problem with other devices though
Just my €0.02!