What I mean is, the key features it shares with the H1N (not the original H1, the new one) are as follows -
Two-channel audio recorder
Supports up to 24-bit/96 kHz audio
Broadcast WAV format (BWF)—files are automatically time-stamped
1.25" monochromatic LCD display can be read under bright light
Stereo 1/8" mic/line input jack with plug-in power (2.5V)
Stereo 1/8" phone/line output jack with dedicated volume control
Built-in limiter and auto level control to avoid clipping
Low-cut filter
Pre-Record function
Tone generator for calibrating audio levels between the F1 and a camera
Sound marker function outputs quick tone for syncing audio and video
Micro-USB port for data exchange to and from computer
Use as an audio interface to record directly to your computer or iOS device
Runs on two standard AAA alkaline, Lithium, or NiMH rechargeable batteries, or AD-17 AC adapter (available separately)
Up to 10 hours of operation with alkaline batteries (when using lavalier)
Card capacity and recording formats are also identical.
Features unique to the F1 are all related to the physical design -
Includes windscreen, belt clip, mic clip
Includes LMF-1 omnidirectional lavalier microphone
Lightweight and low-profile design—attaches to belts and waistbands, or fits inside pockets without being seen
Compatible with all Zoom microphone capsules
Now whether the audio internals are significantly different I can't tell from the available specs, but they may well have simply used the H1N internals lock stock and barrel to minimise production costs. If so, you are paying a fair bit extra for the form factor - which of course may well be something you value.