What are the important differences for games with 3, 4, 5, 6 and 7 players?
This article on BGG is probably the definitive guide on differences with different player counts. To summarize some of its points here:


4p features the most basic (brown) resources per player of any player count. You can wait to draft what you need. By contrast, 3p and 7p have the least resources per player, and in those games you should draft the resource-granting cards you need immediately.
4p features the fewest advanced (gray) goods per player; 3p and 6p features the most; 5p has an average number, but they are concentrated in Age 2.
There are the most science (green) cards per player in 3p, followed by 4p. There are the fewest at 6p. 
In 3p and 7p, the three science symbols are evenly distributed. In 5p, the symbols are evenly distributed, but there are fewer gears early and more later on. In 4p, there are 6 total tablet cards, 5 compasses, and only 4 gears!
In 3p and 4p, there is exactly one military (red) card per player per Age. In 5p, there is one extra in Age 3. In 6p and 7p, there is one red card "missing" in Age 1, but extras in Ages 2 and 3, and overall more shields total.
There is only one of the powerful Caravansery cards (the yellow wild basic resource card) in 3-4p. One is added in 5p and 6p.
There is only one Forum card (the yellow wild advanced goods card) in 3-5p. One is added in 6p and 7p.
Blue cards are always good and you can never have too many.