I'm not sure either of them do, do they?
...Perhaps obsmap does. I think ebird just records the route you traveled whilst recording. So you could calculate an average density along the route but not get the fine scale info about actual encounters within the walk. (Please correct me if this is wrong.)
In each case the data would be somewhat imprecise but a valuable tool for those who are disciplined (e.g. I often add sightings as I remember them along the walk after being distracted by others things: so not absolutely precise). But ability to easily record "one-off" or "incidental" things is one of things missing from ebird. (Could just add new category to "traveling"etc)
Actually, that's one reason I'd prefer to write my own app. Wish one or other would open source theirs: no way I want to develop the whole thing from scratch. Unsure why ebird at least doesn't since it's developed with public money. I'd be happy to submit my observations to whoever wants them then (provided I continue to own them).
[Further edit: I see the mobile app has changed and you can add incidental observations. Think I suggested that to them but didn't hear anything back... Now if they just open source it...]
I thought I would add my thoughts;
I have read through the various comments and it clear that some are down to system and some to the users.
As I understand it, and I stopped using obs around 3 years ago. Each entry has the gps location of the observer tagged. This is not the bird (or other species) which dependent upon how close you are, could be some distance away.
Ebird can be used in a very similar way You can create a stationary list for each species. However you can put a different gps point to the reference if you choose. For example if you were scoping a flock of geese at c1km you can put the location of the flock against the record. However this is not how most people use it - most use a travelling mode via the app and then place all the species seen and counts against a single located place. This is often a hotspot, but is often not. There are recommendations of how to use the options - but it is a question of how many actually comply.
Ebird is not primarily a listing tool, it is a bird recording tool. However, if you look at the data there are many 'stakeouts' for species in there that shows that it is being used to highlight where to see key species. (But note, some sensitive species have their data hidden anyway)
Btw 'incidental' is not about the bird, but about the observers effort.
Also you can download your records in a csv format at any time - not that I have ever been bothered to do.
Accuracy is mentioned elsewhere. There are two aspects of this, species being out in the wrong place or the wrong species being mentioned. Local reviewers (who are all voluntary in eBird - no idea with obsmap) have tools to identify 'odd' records and encourage the submitters to review, justify or change. They do not change records - only the submitter can - but they can flag a check list if there is an issue. These are still visible, but not used for research data. As a casual user, you should be very careful of flagged checklists.
I have used both data sets in the past, although I have not used obsmap for c 12 months and I still use eBird almost daily. Coverage is very different in different countries, but increasing enormously in most have travelled to, and even in the UK. However, for example in 2020 where I live in Hampshire, there are c 250k records submitted for the year, of which 85% are Birdtrack and 10% are eBird, and virtually none for obsmap.
Israel has adopted it as their formal reporting system, as has Cyprus. Every year there appears to be more. For real time updates in the field it has changed the way I look for bird information