I'm still siding with Civ IV, by a huge longshot. I'm hoping Brave New World would change that, but I doubt it.
Off the top of my head (because I haven't played Civ in quite a while), I have 5 main problems with Civ V: the AI, economy, 1upt, diplomacy, and the modding capability.
The AI is insane and it feels like "human like" AI is just an excuse for an awful one, because it is just as likely to win as the Civ 4 one outside of the (IMO) broken UN victory. They never win through war EVER unless they do a huge bum rush towards the player, do surprise cultural victories, or once in a blue moon launch a space shuttle. All of those things were what the Civ 4 AI did as well, and I'm pretty sure even Jon Shafer himself admitted to the issues with trying to make a "human like" competitive AI. My main issue with the AI is that it has no sense of loyalty or friendship and every single one of them backstabs the player some point in the game. That really breaks my Civ immersion, since I dont play to just kill everything, but to make a civilization with its own allies and its own enemies, almost roleplaying as I play. I can't do that at all and the game no longer feels like I was making alternate history, which is really what got me hooked in Civ 4. This should be fairly easy to change if the devs wanted to.
The economy is a little weird in Civ 5. Everybody agrees that trading posts are god awful compared to the cottage/commerce system. That and several other things makes sure I never feel like I am building up my civilization; my country never feels "developed" because all every single city needs is several turns to get it running. Developing my country just doesnt feel the same as it did in Civ 4. I'm hoping the new expansion fixes this.
The 1upt system was really disappointing. As excellent as the current system sounded at first, it was horrible in practice IMO. There are not enough tiles to warrant the type of combat system Shafer had planned and especially later, it just becomes a giant cluster****. Every single AI tile seems to be occupied by a unit and it really becomes a hassle to even organize my armies, considering how awful path finding and those sorts of things are. Limited resources didn't do a thing because theres far too many resources and the bulk of your army later on consists of 0 resource infantry anyways. This is unfortunately never going to change in this game.
Diplomacy is a little botched and it was like that in Civ 4 as well. Its really annoying having to renew open borders etc, and not having trade maps option is really stupid. There is no vassal system which I loved in Civ 4, since I much prefer to have a big confederation type empire with their own independent armies which I don't have to micromanage. Rest of the diplomacy issue is just due to AI issues. Should be easily fixable.
What made Civ 4 for me were mods like Rise of Legends and Fall From Heaven. Unfortunately, it seems that modding is dying on the forums due to lack of support from Firaxis and of course, the awful steam workshop that simply steals potential forum goers and modders. Steam workshop has terrible infrastructure and theres no way there can be any large scale mod projects can arise from such a place; the forums like this one are required for such things to happen. Nothing will change here ever for Civ 5, and quite possibly forever.
Of the five things mentioned here, two should be easily fixable and one of them will be fixed one way or another, through mods or expansions. There are many great things about Civ 5 but this game killed off my Civ era of my life. I still think the game has lots of potential and is salvageable, and it definitely has improved over time, though G&K was kind of a big letdown. I think one day, if Firaxis supports this game enough, it will surpass Civ 4 in a big way, outside of its modding potential of course. Then again, judging by most company's methods these days, Civ 6 would come out earlier before Civ 5 is properly fixed up.