If you have to enter / search / whatever information in an app which is horrible to use (a BIT of lag can ruin your day; you tap/swipe; because of the lag it just responds a bit late, the keyboard pops for the wrong field or you submit accidentally; plop seconds lost and so is your good mood) all day, you're not going to want to work with crap. It's not 'good enough' even though management might think so.
In both cases I still think you are better/easier/happier/cheaper off building it once and in case 1) giving your employees tablets/phones with the target OS and in case 2) just waiting till you have enough critical mass to warrant writing a version for the next OS.
Not to mention that, in most cases we have made HTML5 'hybrid' apps, we noticed that it takes more time making it uniform and smooth across the plethora of (especially Android) devices than just writing 2 native versions. And the HTML5 version will just never work well on a large amount of 'Alibaba $50' Android devices which surprisingly many people have. Resulting in TONS of bad reviews (if public) and/or very frustrated people.
this was going to be my comment on the original comment: it's not like you have to do only HTML5 or only native, or so i'm given to understand... i'd be interested to hear more about the hybrid approach if anyone has links/blog posts.
My take on this is that if you absolutely need the performance, go native and pick the platform you'll get the most customers on. If you're app is a glorified CRUD wrapper, though, HTML5 will probably suit your needs and you'll only have to code it up once.