I like both. They have different feels to me though.
I don’t see [name_m]Nathan[/name_m] as incomplete - it’s a Biblical name in its own right. I hate [name_m]Ethan[/name_m], but I like [name_m]Nathan[/name_m]. It’s a calm sort of name. It’s not stylish OR dated. It’s a very muted, classic feel to me. A bit like [name_u]Michael[/name_u]. It’s as unflappable as [name_m]Luke[/name_m] and [name_m]Isaac[/name_m].
[name_m]Nathaniel[/name_m] or [name_m]Nathanael[/name_m] (I like both spellings) is a bit dreamier and more of a “statement” - for years I loved it more, as it had more impact and drama. I don’t see it as too flimsy or not strong enough - it reminds me of [name_m]Alexander[/name_m]. [name_m]Long[/name_m] but distinctly masculine. It’s accessible, too.
[name_f]My[/name_f] only issue is I don’t particularly like [name_u]Nat[/name_u] or [name_m]Nate[/name_m]. In that sense, [name_m]Nathan[/name_m] is now pulling ahead slightly for me, as its shorter and likelier to not be cut down. But since you love [name_m]Nate[/name_m], [name_m]Nathaniel[/name_m] seems the natural choice to me.