Although I've never personally run a game like this (Swords and Sandals) - I fully intend to.
I think the key thing here is, as always when I talk about these things, is making sure you put your players deep into the context of the world. It's not enough for me to just watch the movies and know the fables, it's about taking all of that and putting it in context with Bronze Age cultures and bringing it all to life. A lot of this stuff is slightly tweaked material from standard S&S fantasy, but with bigger "legendary" stuff.
- the gods (and their enemies) are active! PC's get cursed/blessed which by itself makes them have enemies
- legendary beasts. Go full Kaiju if you have to. Give them fatal flaws, but exploiting those flaws are major quests unto themselves
- ancient cults that have big secrets they protect. Screwing with them makes enemies of various powers.
- Wars! City states are always seeking to expand, or at least crush their enemies!
- Mysteries and Secrets of the Powers. The world looks normal, but there are secret rules known only to the Powers that certain mortals can learn (and abuse). As always, just knowing this stuff can/will make you enemies and friends with other Powers.
- Bronze Age historical fun. Chariot races, gladiatorial fighting, raping the horses and riding off on the women etc.
... damn I'm getting myself all psyched up now...