A faster world is typically a harder world.
In a speed 1 world you can get away with logging on once every 2 days if you aren't at war with someone, it can take weeks to built and army and if you have a low unit speed it will take hours and hours to reach people.
In speed 3 everything is 3 times faster, so initially the world gets going faster. but no, not everyone's city will grow at the same rate. If i log on once every few hours during the day and queue more buildings and you are only logging one once or twice in teh evenings, i am going to grow faster.
Also, because of the faster speed, you can start ot build a slinger nuke (over 1000) on monday, kill them off in an attack on wednesday, and have they rebuilt and ready to go again by friday evening. It is awesome.