While most 13☆s are a straight upgrade over Nox, right now, for almost every class combination, your best choices are Gix, Slave, or Nemesis.
If you can avoid getting hit completely, Gix will give you the highest damage bonus (20%).
Slave and Nemesis both have extremely high RNG-Pwr relative to most other TMGs, and have a 17% unconditional damage bonus. The main difference between them is their defensive abilities, with Slave giving you super armor, +20% natural PP recovery, and +30% attack PP recovery, and Nemesis giving you 40% damage reduction and 20% PP cost reduction.
If you can't afford them, then your best general option is H10 Missouri since it has 14% general damage and +2PP per normal attack.
Oh, also, Mars is really good for bosses, especially if you add its S-Grade Augment since it basically puts you at Gix level without the need to avoid all damage (+12% general damage, +5% against bosses naturally, and +3% more against bosses with S2: Goliathslayer's Resolve affixed, on top of +40% PP recovery against bosses).