Best headphone amp under $400

My Dragonfly Red is good enough from my droid phone to Tin hifi T4 iems  but connect to hifiman he-4xx and it runs out of steam well before I do.

Slightly over your budget, but you should consider Chord Mojo. It's not ultra portable, as in you can't put it in your pocket and go out for a run, but certainly something you can take it with you on trips. You might even find a used one for under $400.

thanks all ended up with dragon fly cobalt, sounds really good. had seen mojo pretty nice too but a bit too large (want to fit in a pocket without feeling it!)

There is no 'best'. Period.

Only your ears will tell you what is 'best'.... for you.

Some people like opamp based amps, some like R2R ladder based ones, while some prefer an all-discrete based one.

Some people swear by tubes while others prefer solid-state.

The best headphone amp is the one YOU like the best at the price you want to spend.

I would recommend some planar magnetic headphones. Although I never listened to them personally, I read that they are truly amazing. Audeze, Hifiman, oppo are some of the companies that I can think of. These headphones should be paired up with an amp for true audiophile grade performance but you can also opt for low impedance headphones if you are looking for a mobile setup.

You can also go for open back headphones. Sennheiser is the first company that I would recommend because of their signature sound quality and well renowned sound signature. Beyerdynamic and audio technica are also awesome.

If you can decide on what to get i.e wired or wireless, open or closed back then you can decide on the company and product.