IMO most people are upset because they're wondering why they can't click the same buttons they did before and win automatically like they did with Civ IV (and with Civ III before it...)
personally I'm upset not because you push different buttons, but because there are still 'i win' button tactics that work even more effectively than the 'i win' buttons in civ4.
Civ3: Spam cities everywhere, road every tile, mine grasslands farm plains and build gigantic stacks of doom with archers > swords > MI (conquests) > rifles > infantry > tanks plus cats > trebs (conquests iirc) > cannons > artillery and you win. Corruption failed to punish warmongering enough to stop it from being the best way to win.
Civ4: Build one or two good specialized production cities, maybe axe rush enemy if they're close enough then build slightly smaller stacks of swords > maces > rifles > infantry > tanks plus cats > trebs (warlords) > cannons > artillery and you win. Maintenance failed to punish warmongering enough to stop it from being the best way to win. After BTS Diplomatic becomes the easiest way to win but is SO easy and lame that people avoid doing it because it takes the fun out of the game.
Civ5: Build three or four swordsmen and a bunch of whatever ranged unit is most practical and you win. Nationwide happiness has failed to punish warmongering enough to stop it from being the best way to win. It HAS managed to increase the year of victory though, creating the illusion that it was more difficult because it took longer. I'm sure you can pull off ridiculous 500AD wins if you just methodically burn every capital with longswords though.
I was told that civ5 was going to make military victory more difficult and add incentives to playing peacefully. I see very few indications that this is the case. Oh boo effity hoo, the city states are crying when you're being a warmonger. I hated civ4 at launch but played it, but the issues at hand are very different. Civ4 pissed me off because it kept kicking my ass for seemingly no reason. Civ5 pisses me off because I am kicking its ass with almost zero effort, it feels more like civ revolution than it does the traditional civ games, as if I can just build a few cities then keep hitting enter until I get a victory video. No tech trades has absolutely crippled the AI especially in lower difficulties. I am consistently at least a tech of units ahead of the AI at Monarch.
In the longrun, I forgave civ4 and eventually came to prefer it to civ3 because the economy made more sense and with BTS the AI became competent enough that I actually occasionally lost games at my 'comfortable' difficulty to strong leaders like Shaka or Catherine.
As for the actual level of complaining, it was way worse from civ3 to civ4 because of the ridiculously buggy launch and because you ran a successful economy in civ3 in the EXACT OPPOSITE way you'd run a successful economy in civ4. As earlier posts stated, it was a trap for old players who didn't bother to do their homework.