The only reward other than bragging rights is the increased challenge.
It's hard to quantify exactly how much harder Epic is, but it's another bump up in monster ACs, HP, to-hit, damage, etc at a minimum, so if monsters aren't surviving long enough to attack, there's a good indication.
One simple thing to add challenge is to not boost your party's Initiative. 10 CoAS and/or Awareness as a scroll usually means the party goes first, which makes a big difference, especially for monsters that have an "opening salvo" AoE ability.
Alternately, if you are playing Nightmare with a group of players that agree and an amenable DM, and you win the first fight in a single round, you could ask the DM to give it Epic HP, or epic AC, without increasing the damage output (if you don't have high ACs/tons of HP/tons of consumable healing).
Or you can play "out of position" i.e. a melee-combat wizard, etc. or do themed runs that are sub-optimal.
If you have the tokens to cake-walk Nightmare, for instance, you could try a Drow run, where everyone wears Drow Armor and uses Drow weapons, but still use all your other boosting tokens.
On the other hand, it's generally not intended for the 1st monster to kill players, or for the 2nd monster to TPK, so you should expect to survive them (with healing), though if you are 1-turning more than one monster, your party is probably too powerful/optimized for the level you're at.
I came here to sing and collect tokens, and I'm alllll out of money.