The Fiio will drive them, but nowhere near their capability. The HE400's would be better for mobile use in that sense as they are more efficient. Having said that I powered mine with a little c'moy once and they didn't sound too bad. But bare in mind that all planars require more power than normal dynamics.
I own HE-400s and I have to disagree. I think they are just like the other HiFiMan planars in their need for a lot of power. I have a Cmoy and the HE-400s are the only headphones that I have tried that do not work well with the Cmoy.
I recently obtained a 1985 Kenwood power amp - 330 watts per channel - with built-in headphone jack and while using that, I realized that it is the first time that the HE-400 have worked properly.
So, why do people say that they work better with less power than HE-500 or other HiFiMan planars ? Simply because they are much less in price, so they are bought by people who do not have the money for high power amps. And most head-fi'ers don't use vintage amps, they want something they can order from Amazon or new from a brick-and-mortar store.
Lastly, if you can wait a few weeks, the new Alpha Dog will start shipping by the end of the month, which is a planar that is $100 less than HE-500 and has been getting rave reviews: