Hahah, I already knew from seeing [name_m]Adam[/name_m] vs [name_m]Jaydan[/name_m], that [name_m]Adam[/name_m] would win - I just read them all - not one vote for [name_m]Jaydan[/name_m], as I expected.
[name_m]Adam[/name_m] also gets my vote - it’s a classic and a really gorgeous, unexpected in these times between all the -ayden/aiden boys x)
I think [name_u]Jayden[/name_u] is just as popular as [name_m]Adam[/name_m]. I personally know more of them than [name_m]Adams[/name_m]. So I would go with [name_m]Adam[/name_m].
[name_u]Jayden[/name_u] is a name that ANNOYS a huge number of people.
Before people even meet [name_u]Jayden[/name_u], they have formed an opinion (made-up name, misspelled, trendy).
I vote [name_m]Jaydan[/name_m]…just kidding, [name_m]Adam[/name_m] is the best option here. Best of luck!
I would go with [name_m]Adam[/name_m] as I’m personally not a huge fan of [name_m]Jaydan[/name_m] and the way it sounds with the last name.
You mentioned you are worried about him going to school with other [name_m]Adams[/name_m]…however, the whole trend of [name_m]Caden[/name_m], [name_u]Jayden[/name_u]/[name_m]Jaydan[/name_m], [name_u]Aiden[/name_u]/[name_u]Aidan[/name_u], and [name_u]Brayden[/name_u] is pretty popular right now so I feel like there’s a chance of him running into more Jaydans, though the spelling may be different, than [name_m]Adams[/name_m].
The pronunciation thing is also a big factor to me. It may get confusing having it pronounced two different ways whereas he wouldn’t have that with [name_m]Adam[/name_m].
With everything you said, I sincerely feel like [name_m]Adam[/name_m] would be your best bet.
Good luck.
I vote [name_m]Adam[/name_m].
It’s strong and classic. In my area, it’s overlooked, and I haven’t heard any child named that.
Plus, I know what it’s like to have to correct mispronunciations ALL the time, and after a while, you give up in frustration lol.
[name_m]Adam[/name_m]. It’s not really that common in actual usage and its a strong, handsome, classic name.
[name_m]Jaydan[/name_m] is super trendy and will be misspelled regularly.
My vote is definitely for [name_m]Adam[/name_m]. 
[name_m]Adam[/name_m] is the clear winner. I don’t think it is remotely as popular as you think it is, and it is far more handsome and strong than [name_u]Jayden[/name_u].
Good luck!
Definitely [name_m]Adam[/name_m]! [name_m]Rollo[/name_m] had it right. [name_u]Jayden[/name_u] and all other [name_u]Aiden[/name_u] names are very trendy and passé. [name_m]Adam[/name_m] is such a handsome timeless name. I have only met two [name_m]Adam[/name_m]'s in my entire life. [name_m]Don[/name_m]'t let your son be lost in a sea of [name_u]Aiden[/name_u]'s!
[name_m]Adam[/name_m] is such a classic and very handsome. You can’t go wrong with [name_m]Adam[/name_m]!