I didn't poll the fandom or anything. I guess I just got the impression the GCW was more iconic then the Fall of the Old Republic/Clone War Era based on media around it.
I'd argue that the GCW is the more iconic war, while the Clone Wars is the more popular war. That may seem like splitting hairs, but I'll put it this way.
If I say "Star Wars" to the average person, they're almost certainly going to think of something from the OT first. By extension, that would include stuff like the Death Stars and Hoth. This material has been burnt into the popular conciousness for decades. Or, in another sense, everyone knows what a stormtrooper is. A clone trooper though? Not so much.
However, within the fanbase, the Clone Wars have struck me as the more popular conflict. I don't have hard numbers, but I've noticed that the clones have kind of achieved a kind of affinity within the fanbase that the rebels/Empire never have (more on the clones later). Also, there's the Clone Wars series itself. I'm not aware of any Star Wars transmedia campaign that's achieved the same level of popularity that the Clone Wars have - remember the Shadows of the Empire transmedia campaign? I didn't even know it was a transmedia campaign until decades after playing the game on the N64 and thinking it was some random game. I know that's not a 1:1 comparison, but what's achieved the level of success as the Clone Wars? Not Rebels. Not Resistance. Sure as hell not Droids or Ewok Adventures. The only thing that comes close is KOTOR, but that's contextually different.
The clones I totally get. Not only did TCW flesh them out to be likable and have different personalities and such, but there's the inherent tragedy there of how they were basically bred as a cannon fodder slave army for a war that was a farce to begin with and as soon as it was over, they'd be forced to murder their generals who they'd fought alongside for years before being discarded themselves (presumably, considering we don't see a lot of clones left by the time Rebels starts).
So, the thing about the clones. On one hand, I get the popularity. On the other, I kind of disagree with it.
Here's the thing, from my perspective, as someone who's never been that into the Star Wars EU. Taking the films by themselves, there's very little to suggest that the clones have distinct personalities, and what does exist indicates that they're little better than droids. In Ep. 2, there's not a single clone character. In Ep. 3, we know there's a bit of friendship between Obi-Wan and Cody, but as soon as Order 66 is given, there's nothing to suggest that any of the clones have any compunction against turning on the Jedi. Yes, Cody does have a throwaway line in the RotS novelization about firing on Obi-Wan, but that's it. The way I saw it was that we aren't meant to sympathize with the clones. We're meant to see them as amoral soldiers that, putting two and two together, go on to be the stormtroopers - the visual elements in RotS is enough to establish this. Now, that's not to say you couldn't hypothetically tell stories about clones that gained free will, and those stories were told, but to me, those stories would be the exception rather than the rule.
Of course, the Clone Wars TV series, and a plenthora of other media (e.g. the Karen Traviss Clone trooper novels) make an effort to 'rehabilitate' the clones, in that a lot of them gain personalities. The ethics of their creation are questioned, Ashoka becomes friends with Rex (or according to fanfic, something more), and I've seen the Order 66 Clone Wars clips, which are like night and day compared to how RotS portrays them. Now, you could argue that this makes the clones more interesting. That it adds moral ambiguity to the actual conflict, that the Republic is breeding sapient beings to fight a war against a force that is fighting for independence. If you said that, maybe you're right. I can't deny that it arguably adds depth to the clones. However, I would maintain that how the clone troopers came to be portrayed in media, is VASTLY different from how the films portrayed them.
Also, there's another thing that I find a bit puzzling about this. EU media has humanized the clones, and the fanbase seems to have liked it, given the popularity of various characters. However, that humanization hasn't been extended to stormtroopers or even droids. Oh sure, some stories have dealt with stormtroopers going rogue, but never to the same extent, and I can't think of a stormtrooper character that's ever achieved the popularity of clone trooper characters. Heck, say what you will about the sequel trilogy, but it at least gave us Finn, and Jannah, and humanized stormtroopers to an extent. But again, it seems that we're willing to humanize one group of faceless soldiers (clone troopers), while laugh at another (stormtroopers). And droids? Solo treated L3's liberation attempts as a joke, and even then, some fans accused the film of being "SJWed" because a female droid was trying to get other droids to seize their independence.
So, yeah. On one hand, I get the clone troopers' popularity. On the other, I also don't.