Great questions and great responses all around. I came to iNaturalist after eBird. I struggle(d) with the some of the same questions but in the last few years here are the personal patterns that have emerged around my daily usage of both sites:
I do daily checklists on eBird, sometimes multiple lists at different times of day in the same location and sometimes several lists in several locations. My personal interest in doing these lists is to get a feel over the years for some very specific bird behavior, timing, patterns etc. for my “patch.” and to be able to eventually look back and evaluate trends and changes out of curiosity. Hopefully, I’m helping scientific research in some way too by having clear occurrence and count data.
I also make almost daily observations on iNat of other organisms and include birds when: 1) I want to document a special sighting (special for any number of reasons) with or without photo and 2) if I capture a verifiable photo of the individual. The other factor in deciding to add bird sightings to iNaturalist is that I can search my observations very easily whereas I find eBird lists highly difficult to find without scrolling and searching for a long time. So, if I see something that I have a lot to say about or want to remember and be able to easily locate, I will use iNat.
I do duplicate my observations occasionally and I never make a bird observation on iNat without having submitted it to eBird as well.
The exception to this rule is in places where I have no service because I can take a photo in iNat and it will record my location but with eBird, creating an offline checklist doesn’t always work and then I get frustrated. In such cases, I will just use iNat.
Not being able to add photos with the eBird app is another motivator to post birds to iNat. Aside: I also feel totally unwelcome in posting my low-quality photos to eBird so only really do so if I have captured something interesting or rare (i.e.: proving we had a western tanager, etc.).
If iNat eventually had some way to incorporate eBird style bird checklists complete with counts, easy scrolling breeding bird codes, etc. (to capture the data @fogartyf was explaining) I would probably not have much to do with eBird anymore. I try to add observation fields for my bird obs on iNat but that’s recent. eBird’s advantage is the easy drop-down with no extra steps to record BBCs and numbers. I wish both apps (iNat and eBird) had more annotation accessibility in the app.
I get a million times what I put into iNat back out of it and for me eBird is something I give data to but don’t get much from because I don’t spend much time on the website and they’re very much a one-way street community-wise.
Overall, I think that until iNat can capture the data that eBird does, I’ll continue to use both daily and I hope you consider submitting in both places. iNat is way more engaging and fun for me and I’m constantly pulled into more involvement whereas eBird is a thing I do to be part of a citizen science effort and not much else.