Size of Empire
http://picard578.blogspot.com/2010/11/sw-galaxy-size.html
Also:
http://www.st-v-sw.net/STSWcompare.html
Size of Federation
In Dominion War we have projected casualties of around 900 billion. That suggests 1.2 to 2 trillion population, which allows for 200 to 500 relatively heavily populated planets. My estimate for human population is between 35 and 70 billion, 50 to 60 billion optimum. That would mean humans count for 1.75 to 5.8 % of total population.
From First Contact we know that "there are 150 planets in Federation, spread over 8 000 light years". Given that Kirk says that "humanity is on thousand worlds and spreading" over century earlier, I would take quote of 150 planets to mean full members, with unindentified number of colonies, probably some thousands.
Territory comparation at my site.
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