I dunno, as a long time civ player I think Civ IV, especially with both expansions, is as good as it's ever been, by far.
1. Unit promotions allow you to customize your units. A good thing. You can adapt them to your strategy, terrain, situation, whatever. There is no one unit to dominate with. You can't just build one type of unit. There is choice, and choice driven by strategic thinking.
2. Religion isn't really neutered. It's actually very powerful and meaningful. It ties into wonders, strategy, and most importantly diplomacy. Religion is a factor that gives meaning to AI decision making and behavior and game flow. Instead of AIs doing random things, like randomly declaring war, they will often do so instead for reglious reasons, or due to blocks of AIs forming pseudo-alliances due to religions. Religion adds a ton to the game just in the diplomatic ties. Religion also ties in to civics, commerce, wonders - lots of things.
I think it's cool that in many games civs will settle and align in blocs, largely driven by religion, that can affect the entire course of the game, increase the "every game is different" factor, and give each game a lot more personality. This is vastly superior to Civ I-III where you just had a world full of civs with no real relationships or reasons for behavior.
I played a ton of Civ III and often hated how random and erratic the AIs were. AIs in Civ IV are usually way less erratic and much more logical in behavior. Religion is often (but not always, or it'd be equally lame) a big factor - and as a player, you can help forge or at least understand why an AI is doing something beyond a random dice roll causing a world war.
The ones who say religion is neutered are the ones who want the named religions to have certain powers or abilities and whatnot, which makes no sense in this game design, because the powers and abilities are selected by YOU in how you choose your civics, what wonders you build, and stuff like that that leverages your religion. Not to mention that it would be insensative and volatile to presume to tie certain behaviors or abilities to certain religions. If you as a player want Judaism to be a violent warmongering religion then it's up to you to found it, pick warlike religious civics, go to war, and live that selection - it's not up to the game designers to say that 'religion x' gives such and such bonus to war.
Religion is far from neutered in Civ IV!
3. The civic system in Civ IV is by far the best ever - because it lets you choose how to run your civ rather than being forced into narrowminded pre-selected and limited "sets." Strategy gaming is all about having and making choices. The more wide open and fully customizeable civic system in Civ IV leads you to making lots of choices - a very good thing. The civics system also ties in to the different victory paths, since often your civic choices are very supportive of your road to victory - but at a cost since they can hurt you in other ways. The top level choices in the Civ IV civic system are not always the best option - it all depends on your strategy. The game doesn't force you to constantly upgrade your civics (unless you happen to select 'yes' every time you research one and are asked if you want to change!)
Civics can also tie into diplomacy. An AI might like or dislike you based on your civic choices. It's another way to get AIs to behave and act for a reason instead of doing things randomly.
4. The tech tree in Civ IV is different. I'm not sure I'd call it strange. As I find myself pointing out repeatedly to people who should already know this - Civ is a game - not a historical simulation. There's really little reason to get hung up on historical inaccuracies in one smidge or even one aspect of Civ, since the game is only historically flavored and not meant to recreate history. The tech tree is meant to be historically inspired and balanced for good gameplay, not historically accurate.
I think the early ages can whiz by in all of Civ - it's not faster in Civ IV - and it really has to do with how you're playing. If you're a warmonger at any time the game slows up. If you just turtle the game flies by regardless. Civ IV also offers a variety of game speeds. If you play on epic or marathon the game stretches out nicely and units/structures from each time period have longer lives.
I also think pace has a bit to do with how expansion occurs. Depending on the setup, you could easily be settling for ages in Civ III, because all you did for a long time was to settle every piece of land you could get to. Civ IV slows down the settling by making it increasingly expensive, so you usually end up plopping down fewer cities initially and needing to research and develop infrastructure to support more expansion, and this could give the impression a faster game because you're not managing so many settlers or so much expansion.
5. I don't see a difference in game pacing with Civ IV and I don't see the AIs being "in cahoots".
Civ IV is not Civ III. It can take a while to learn it, since you're basically learning a new but familiar game.
6. IMO, saying you're a veteran of Civ I-III doesn't mean much when it comes to Civ IV, other than to express that you're a fan of the series. It doesn't automagically mean you'll be good at Civ IV or anything like that.
The best advice one can give, I think, is something that was said a lot when these kinds of threads came out in the early days of Civ IV. And that is, treat Civ IV like a new game and open your mind up to learning how to play it. Civ IV isn't just a Civ III expansion with pretty graphics and a few new features. Civ IV is the spirit of Civ with many systems completely reworked for (much) better gameplay. Civ IV is more about doing things based on logic and reason instead of "this is how the game does things."
edit: Sorry, I'm sarky today. Take my posts as more blunt as they should be for polite conversation. 
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