SELECT ... FOR UPDATE SKIP LOCKED is purpose-built for this and is what most Postgres-backed queues use:

1UPDATE jobs SET status = 'running', worker_id = $1
2WHERE id = (
3  SELECT id FROM jobs
4  WHERE status = 'pending'
5  ORDER BY created_at
6  FOR UPDATE SKIP LOCKED
7  LIMIT 1
8)
9RETURNING *;

1UPDATE jobs SET status = 'running', worker_id = $1
2WHERE id = (
3  SELECT id FROM jobs
4  WHERE status = 'pending'
5  ORDER BY created_at
6  FOR UPDATE SKIP LOCKED
7  LIMIT 1
8)
9RETURNING *;

SKIP LOCKED is the important part — without it, workers queue behind each other on the same row and throughput collapses to serial. With it, each worker takes the first row nobody else holds.

Advisory locks are for coordinating things that are not rows (a nightly job that must run once across the fleet). For claiming rows, they are strictly more bookkeeping.