Fanatic, 2X bonus vs all infantry & Cavalry.(anti-infantry is included) They beat all human units one by one except war elephant. However, they are beaten by anti-infantry, such as axemen, hypaspists & TA(so sad...TA need to MASS), MASS archers, such as CA, Tox & Arcus population and cost wise.
Myrmidons, 1.5X bonus VS all non greek units except TA & axeman. They beat all human units one by one except war elephant and Fanatic. They are slaughted by all hard infantry counter, axemen, hypaspists & TA since myrmidons do NOT get any bonus vs them. Also, they are beaten by Hoplite & Mass Tox population and cost wise. They are ok vs all non-greek archers due to 1.5 bonus. However, MASS non-greek archers with meatshield can beat myrmidons.
Note: Myrmidons are much easier to mass than Fanatic because they are available both in Military Academy and Fortress in mythic age.