Card Game: Redraw vs. Switch Option

Two players each draw one card from a well-shuffled deck of 100 cards numbered 1 through 100. The player with the higher card wins the difference -- if you hold card $c$ and your opponent holds card $d$, you collect $c - d$ dollars (negative means you pay). Before the game is resolved, you are offered one of two options (you must choose exactly one): 1. **Redraw option**: You may put your card back, the deck is reshuffled, and you draw a fresh card. 2. **Switch option**: You may swap cards with your opponent. Neither you nor your opponent can see each other's card when you decide. (a) Which option should you prefer? (b) How much would you pay for each option separately, before drawing your own card?