Ok more weirdness, it's fixed itself. Might be that I poked around in the settings (didn't change anything), viewed and edited a note (as a test) or maybe just waited long enough for some background thread to finish.
Very similar issue for me. I can interact with existing notes but new notes cause a crash. I have been able to temporarily work-around by deleting and reinstalling Evernote. Device restart doesn't help. Might be that the data is exceeding a limit new to iOS 10? I have 70GB free on my device (iPhone 6). After a reinstall, it has to redownload the cache so maybe it works until the cache gets to a point. Attached screenshot of storage screen in iPhone settings Please fix, I love Evernote! Matt