I hear most of the difference in the high frequencies, basically the hihat/cymbals and the snare. In the words of someone who PM'd me: with the F3 source, the upper mids are clean and sharp and the high end is silky and extended.
The warm mod is just a little bit softer, the highs don't jump out at you like the F3 but still very pleasant. I've been on an analog kick lately, thanks to goodcookers cassette project as well as listening to a lot of Mike Millard recordings, and it makes me appreciate what Doug tries to do with these mods.
I hesitated to put the "vs" in the title, as it's not a competition to me but a presentation of options. But I knew both would sound good and was hoping to open people to both: the Zoom F series recorders are not the junk/toy recorders of years ago but serious options. The Oade mods are not snake oil but still relevant, especially if you want different "flavors" for different scenarios.
I plan to keep my warm mod 661 primarily for outdoor recordings, particularly bluegrass. When I first got the 661 I ran it indoors for a jazz show where I was really close to the stage and it is such a wonderful recording with huge soundstage.
I did NOT start hearing these kinds of details until I upgraded my playback. I'm soooo fortunate to finally get out of apartments and now I have a dedicated listening room with sound treatment. In my not-so-humble opinion studio monitors are the best way to listen to audience recordings

I've heard some awesome home theaters/playbacks but they tend to color the sound; I want to hear my gear transparently. For my living room I even picked up some used Presonus bluetooth 4.5 inch monitors to run from a phone or laptop and they're great. If you're still in apartments, start with a entry level DAC/headphone amp and some decent cans. You don't need to break the bank IMO. Look on Facebook Marketplace, the amount of people who tried (and failed) to start a podcast or home studio are endless these days.