Before starting a Last Stand mission you get to choose between playing on Normal or Expert mode. The difficulty is only chosen for that specific mission, which means you are not commiting to one or the other for the whole Last Stand cycle.

Expert mode features all regular survivors, and a pool of 10 random Heroes from which you need to choose your team members. The randomized pool of Heroes is the same for all players, and refreshes weekly.

Expert mode starts from a +10 offset level of your three highest level survivors in your roster, or your highest equipment level minus 3 - whichever is higher.

Scores, Rewards & Leaderboard
Playing Expert mode automatically gives you a multiplier to your total score, and since you start a Last Stand mission at a higher level, the wave rewards are also increased.

The same leaderboard is shared by all players, but if any of your top 3 scores are obtained from Expert mode, you will have an equivalent number of Expert badges attached to your leaderboard position and score.
Eg. If all 3 of your top scores are done in Expert mode, you will see three Expert badges together with your name and score.

More details on scoring on a general level in the "How does scoring work in the Last Stand" FAQ.