I rank Barnett over Velasquez and dos Santos, personally. Barnett's longevity in the game is insane and I think he should definitely be seen as one of the Top-5 greatest HWs up until now. He is fighting in his 3rd era of HWs and is still Top-10.
He was a Top-20 HW at the start working his way up (at the time of the Rizzo loss). His win against Schilt catapulted him up to Top-3, only behind Nogueira and Couture. Then he stops Couture and cements himself as the #2 HW in the world for a while until Fedor's rise, which bumps him back to #3. He had some great wins but just could never really beat Filipovic, and those b2b losses brought him down but he was still Top-10. He fought his way up back to Top-3 after the Nogueira win (only fighter besides Fedor to beat him in PRIDE), but also had solid wins over Alexander and Hunt.
Cro Cop beats him again after Barnett goes through the greatest HW fight of all-time while Fiipovic had an easier schedule. He fights Nogueira again to a very close fight. He didn't fight for a while after that but when he returned he had a solid winning streak up until the Cormier fight (still believe that fight would have looked a lot different if Barnett didn't break his hand in the first 30 seconds). Then 16 years from his debut he puts on one of the finest performances of his career, completely dismantling Frank Mir. He had a poor showing against Browne but he is still one of the few elite HWs in the world.
1999-mid 2001: Top-20
2001-late 2004: Top-3, peaking at #2 before Fedor fought Nogueira
Late 2004- early 2006: Top-10
Rest of 2006: Top-5 the whole year going 5-2 with losses to a better conditioned Filipovic and a very close fight with Nogueira, was Top-3 for a couple months and peaked at #2 for the year, behind Fedor
2008: Top-10, arguably Top-5
2009-2016: Top-10, shifting up and down depending on wins from other fighters, around the 6-8 range in the later portion
The only other HW with comparable longevity is Nogueira who he is 1-1 with (in their primes, and he was definitely closer to winning in his loss than Nogueira was). I rank their peaks very close to each other and think you could argue for Barnett in terms of skills, even though Nogueira was considered the best HW in the world at one point while Barnett never was. Just look at his wins, schedule, and performances ... The only 4 guys he fought and hasn't beaten are Filipovic, Cormier, Rothwell, and Browne. Three of those guys he hasn't rematched (yet).