How is game feel and strategy different between the 1st and 3rd edition scoring rules?
I prefer the new rules for the simple reason that farmer scoring always used to be a huge headache.  Doing it pasture by pasture, with the ability to simply empty the pasture of farmers once it's been scored, seems like a great timesaver.  It also feels good that pasture rules have fallen pretty much exactly in line with city-scoring rules.

When I found about the rule change, I was a bit miffed about the new city scoring.  It seemed excessively cheap to be able to make a size-2 city and score 4 for it without any meeple investment.  The added consistency is welcome, though.  It's annoying when teaching any game to new players to have to say "the rule is this... except in this situation, when it's this".  So this change is probably a score draw at worst.

How do the changes alter things strategically?  Well, now that small cities are twice as attractive an option, you're going to get a lot more of them.  More cities equals more opportunities for farmers to make big scores.  That being the case, it's probably good that the farmer rules have been simplified; no one wants a game that makes their head hurt.  Well, most people don't.  (A lot of my friends love Ricochet Robots.)

Simplified-rules Carcassonne retains the excellent central dynamic of the game - between scoring points on the board throughout the game, or building up a farmer presence that will allow for a big score at the end.  Novice players generally don't really get farmers, and I've often found them disappointed when they get crushed in the final tallying-up of a game they thought they were holding their own in.  By keeping farmer rules simple enough that they have a chance of understanding them during their first game, everyone is more likely to be happy.  Farmers may still be the weapon of choice for the Carcassonne expert, but explaining how exactly you won with them no longer feels so dirty!