For me, CivIV does not have the "epic" feel that I love about Civ4. It just can't handle the same sized map as easily, and really big ones are pretty much out of the question. With Civ3, you'll eventually be reminded by the in-between-turn times that you're playing a really big map, but even on a moderately large one you can get a very "epic" sense with Civ3.
And the claim that Civ4
supports larger map sizes, while perhaps technically possible if you can avoid Memory Allocation Failures (unlikely), is based on false claims. Sirian quotes the Civ3 Huge map size as 160x160; that's the nerfed size in Conquests. In vanilla Civ3, Huge is 180x180, giving 16200 tiles, a 10% bonus over Civ4's largest Huge. And it's at least as playable as a Civ4 Huge with 18 civs. About the largest Civ4 map I can find reference to is 192x120 (23040 tiles); a 220x220 Civ3 map at 24200 tiles is still playable (probably more so) and unlikely to hit the city limit. I'd care less about this if the Civ4 box hadn't advertised the larger maps.
Civ4 also seems to have a slower build pace for units, which also hurts epic-ness in my opinion. Granted, that's moddable, and I started to mod that once, but never completed that mod.
There are several other issues I have with Civ4, such as the inability to bombard properly as you can in Civ3 (you can't destroy buildings in a city with bombing?!?!? no ranged bombardment of units/terrain outside of cities???). The ineptness with which my computer played Civ4 when I bought Civ4 also likely has had a long-term impact on how much I like Civ4 - and it certainly negatively impacted my view of Civ4's epicness (thought I still think Civ4 is considerably less epic, even though I can now play Civ4 quite well on my computer).
I do plan to actually dig into Civ4 now that I have Beyond the Sword sometime, but there's still a lot of community mods I haven't tried for Civ3 that I want to try as well. That's in part due to not having Internet for 3 years after getting Civ3, but also because the epic game in Civ3 had much greater replayability for me than that of Civ4. And there's still new mods coming out for Civ3. Civinator's CCM is near the top of my want-to-try list, and I hope to try it this summer.
I don't know that Civ4 will "disappear" anytime soon, but it will be interesting to watch the effect of Civ5. In part, of course, it depends on how well received Civ5 is, which we can only speculate on at this point. I might switch to Civ5 if it really seems to hit the mark for me, but I'll probably try the demo before buying, after Civ4 failed to meet my expectations. If it doesn't hit the mark for me, I know I've still got plenty of Civ3 content to last several more years. Especially as I don't play as many games as I used to, either overall, in the strategy genre, or of Civ.
A number of my real-life friends play Civ3 as well, and I was in a Civ3 LAN with several of them over New Year's. Some, but not all, of them, still play Civ4 (one still has Civ2), and one still plays CivRev. The few of them that didn't play Civ3 in the pre-Civ4 days didn't put up much resistance to trying Civ3 given its bargain price these days and reputation - and none of them have expressed regret at buying it.
