There's certain things the JH13 (or any custom IEM) will be unable to do vs a full sized phone.. like use the outer ear the way a full sized phone can (i.e. HD800) to present a larger soundstage space.. but in terms of pure detail retrieval, tonal accuracy, speed, accurate imaging/instrument placement, etc., the JH13 FP doesn't, in the slightest, play second fiddle to the HD800, IME. One of the reasons I actually sold the HD800 was cause I realized that I prefer to use IEMs when I'm in the mood to listen with an ultra-resolving phone. Isolation plays a big part in that (for me). Also, the HD800 deserve some pretty nice upstream gear considering how well they scale.. while the JH13 need nothing more than a HQ portable DAC (like the ODAC) & portable amp (like the UHA-6S MKII) to show you just what it's capable of.
Being an owner of the JH13pro for 4 years, couldn't agree more with FlySweep's comments.