RME products are known for transparent conversion without adding anything unwanted to the sound.

When I conducted my first headphone comparison test
   https://www.tonstudio-forum.de/blog/Ent … ADI-2-Pro/
   Direct link to PDF: https://www.tonstudio-forum.de/attachme … -v1-0-pdf/
I suddenly had six headphones in front of me, and I was glad to have a total of eight headphone outputs available for testing (thanks to the UFX+, 2x Octamic XTC, and ADI-2 Pro FS).
All of which performed at a high level in terms of performance and sound quality. At least they were all good enough to initially determine which headphones I preferred in terms of sound characteristics, spatiality, and comfort.

Please note: the differences between the individual headphones in terms of sound and music representation are more significant than minor differences in converters or D/A filters in reference converters.

If you're not satisfied with the sound, I believe switching headphones would make more of a difference. There are superb planar headphones that I've truly enjoyed overall. They have a thin, flat membrane that is suspended between two sets of strong magnets. By their special design, they have low mass, less impedance and thus have advantages in terms of Bass presentation and dynamics overall.

What I'm trying to say is that the differences in sound between the headphone outputs of BBF Pro vs. Pro FS are likely to be minimal. The slightly higher power and slightly lower output impedance of the BBF Pro FS will only make a difference if the current BBF Pro just needs that slight extra power to drive your current headphones loud enough.

If you're still limited by other factors, you might consider upgrading to a UCX II, which has nearly the same output power for headphone outputs as a UFX II and III. These devices, along with Room EQ, now also offer Crossfeed if that feature is of interest to you (before you found this feature only with the reference converter, ADI-2 DAC/Pro, etc.).

Furthermore, you could consider integrating one of the reference converters into your setup. In this case, you could keep the Babyface Pro just in case you require it for mobile applications. See my blog article here to this topic: https://www.tonstudio-forum.de/blog/Ent … our-Setup/
This gives you even more interesting features for your overall monitoring, if the ADAT output is not already being used for other purposes. Browse through the manual or check my blog article to get an idea what features you would get additionally.

Here the differences and features of ADI-2 DAC FS and ADI-2 Pro FS R BE:
https://www.tonstudio-forum.de/blog/Ent … ses-EN-DE/
And if you want to see what the ADI-2/4 Pro FS delivers more, then check this overview:
https://forum.rme-audio.de/viewtopic.php?id=32506

You didn't tell, what headphones you have. Therefore, a general recommendation to think about investing in better headphones. From my experience, planar headphones are generally worth a try. High quality and dynamic and by design a not too high output impedance.

Ideal paired with one of the reference converters. ADI-2 Pro FS R BE and ADI-2/4 Pro SE would also provide you with two additional analog inputs and many useful features.

Good point, thanks Oli Between BBF and BBF Pro FS, the difference is much bigger.

Nevertheless, the integration of ADI-2 DAC or Pro FS and using planar headphones could improve more compared to getting the BBF Pro FS alone. Furthermore, worth noting, the ADI-2 series of reference converters have a special design regarding SteadyClock FS implementation. No matter if the ADI-2 DAC/Pro is clock master or clock slave to the old BBF, the AD/DA conversion is always being performed by using the internal FS clock.

In this case, my Excel overview can give him a better overview of the differences between those USB based recording interfaces: https://forum.rme-audio.de/viewtopic.php?id=35156

Furthermore, the RME product page, which lists the very interesting improvements between the BBF Pro and BBF Pro FS alone:
https://rme-audio.de/babyface-pro-fs.html

that's correct, I currently own the original BBF, and am considering the BBF Pro FS now, due to its small footprint on a desk and mobility.  I also own some planar headphones, Audeze MM-500, which I am wondering if they will sound significantly better with the BBF Pro FS as compared to my BBF.  The volume I get from the BBF headphone amp is good, (no issues with that), I am just wondering if the BBF Pro FS will make the headphones sound much better?