While doublek666 summaries the rules changes between 1st and 3rd editions very well, now I have had a few games, it's worth pointing out how this translates into differences while playing. The biggest difference is that it is much, much easier for a marine player to hold a perimeter. The new sustained fire bonus on overwatch (5+ instead of 6+) and the reduction in cost to clear jams means that if the marine player just holds back 2CPs then it is nearly impossible as the 'stealer player to break the perimeter. (Whereas in first with persistence and whole bunch of 'stealers you could break the perimeter). Two other factors help here too, the new 'guard' stance and the fact you usually have more more command points due the new ability to redraw the CP token if you don't like the first.
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We had one game where the Sargent with the thunder hammer and storm shield was on 'guard' protecting a key corridor. He must have mulched some 25 'stealers before one eventually killed him - it suddenly became the point of the whole game . Not sure of the mathhammer on this one but it is now very hard to break down a well set up perimeter.