La regla · The rule
Concession is the move that makes an argument sound grown-up: you grant the other side something and keep your own position anyway. Pero is the plain one. Sin embargo is however, and it opens a sentence with a comma after it.
Y también · And also
No obstante is its formal twin, meaning nevertheless: no obstante, las cifras cuentan otra cosa. Aun así (even so) is the spoken one. B2 writing that never concedes reads as a list of opinions — la postura (the stance) has to be earned.
Ojo · Watch out
sin embargo and no obstante open a sentence and take a comma after them; aun así sits anywhere. In formal writing, reach for sin embargo before pero at the start of a paragraph — and never write sinembargo as one word.