Does the choice of ship affect difficulty?

Solution 1:

There is no difference in the "difficulty" (number/frequency of enemies, pickups, etc.) when playing with different ships. The only effect that the ship itself has on the difficulty of the game will be due to layout of the ship (e.g. not starting with a shield can make the stealth cruiser tricky to play with; conversely, I've always found the Crystal Cruiser to be a very strong ship).

Remember that large parts of FTL are randomized and so the difficulty will be different for each play-through -- some play-throughs will reward you with good drops and some will punish you with more difficult encounters.

FTL does increase the difficulty of ships from sector to sector -- ships you encounter in later sectors will (on average) be more difficult than ships you encounter in earlier sectors.

Solution 2:

Some ships are easier to start with than others due to how they are configured, but there is no hard-wired "this ship makes the game more difficult". I think both Fed Cruisers have solid to strong starts.