Between those two Halo 3 was easily "bigger", but CoD4:MW certainly kicked-off, or is massively responsible for, the popularity growth of the CoD franchise which has honestly dwarfed the Halo franchise since Halo 3.
I can admit that CoD4:MW is the first FPS title to draw a sizable amount of my own attention away from the Halo franchise and on a fairly regular basis. Just as Halo: Combat Evolved drew my friends and my own attention away from what we considered the "biggest" and "best" FPS titles prior to its release. This would be the N64's GoldenEye 007 & eventually Perfect Dark. Now, there were other titles that we messed with during the time period of GoldenEye 007 and eventually Perfect Dark such as N64's Quake II, the Turok titles, & even South Park; plus, Quake III Arena & Unreal Tournament on the Sega Dreamcast, but they were all just cursory experiences that quickly got left behind as we returned our attention to what we enjoyed the most. The Halo franchise took that top spot pretty much immediately after Combat Evolved released and we all bought our own Xbox consoles in order to system-link them. Again, there were several FPS titles that we occasionally messed around with to try out a new experience, but they were always temporary blips before returning to Halo. The most noteworthy title was Return to Castle Wolfenstein because there was a period of time prior to Halo 2's release when we got Xbox Live (in anticipation of Halo 2's release) and found a lot of enjoyment playing it online, but as soon as Halo 2 released we pretty much stopped playing Return to Castle Wolfenstein. We also played a good amount of Xbox's Halo: Combat Evolved online via XBConnect, but connection quality was always extremely spotty. There were plenty of FPS titles that we dabbled with during Halo 2's primary life-cycle, but none of them were anything but momentary curiosity experiences.
When CoD4:MW released on the Xbox 360 I didn't even get it until after X-mas thanks to being available at a discount and having a few friends who were praising it not only for its' multiplayer, but its campaign too. I had owned Call of Duty 2 and 3, among many other FPS titles leading up to Halo 3's release so I was fairly accustomed to the general game-play it offered, but I never really felt the franchise or those types of FPS titles were "better" than what Halo offered. I mean the CoD campaigns had been fun and the multiplayer was okay, but they never really captivated my, or my friends', attention over Halo. Modern Warfare was different though. Now, I still played the crap out of Halo 3 and it was easily the top game for myself and friends, but over the next year I found myself splitting my time between the two titles more often. I'd say that CoD: World at War may have even made Call of Duty about 50/50 with my play time before Modern Warfare 2 had me actually playing CoD more often than Halo despite some resurgence by adding ODST as a combined alternative. One of the big reasons was that the majority of my Halo friends had converted over to the CoD franchise as their favorite FPS experience and another was the frustrations that were mounting because of quitters within Halo. I thought that Reach would bring the majority of us back to Halo, but sadly its multiplayer was pretty disappointing. The campaign was fairly solid and the customs were actually amazing (this is where we spent a good amount of our time), but there was no denying that in general Halo had fallen behind CoD for myself and most of those I gamed with. Nevertheless, I still played a decent amount of Reach multiplayer (often solo) and continued to play some Halo 3 too, but not as much as I played CoD titles of Black Ops, the Modern Warfare titles, and World at War (a personal favorite). Not to mention, I also started to find some real enjoyment with the Battlefield franchise too which started with some occasional play of Bad Company 2 with a new friend, but my interest truly grew with Battlefield 3. I even gave Crysis 2 a decent amount of solo play around this time period.
It was Black Ops 2 that ended my enjoyment with the CoD franchise. I didn't like the the future aspect and the multiplayer experience felt pretty lackluster IMO. At this time Battlefield 3 and Halo 4 had risen to the top of my personal FPS interests. Most of my real life friends continued playing Call of Duty as they didn't find much reason to return to Halo and didn't care for Battlefield or Crysis. Many also simply moved on from playing video games in general because they were in their 30s and had family responsibilities (spouse/kids/whatnot). While the MCC seemed like it would bring several of them back to gaming and Halo it didn't last long thanks to the broken state of the game. While I personally love Halo 5 most of my older Halo friends didn't stick around with it beyond its first year or so for a multitude of reasons. Nowadays CoD, Overwatch, Destiny, Battlefield, Far Cry, Titanfall, Battlefront, Doom, Fortnite, etc. all manage to pull people's interests away from Halo. It is quite the competitive market. I find enjoyment with a majority of those titles too, but I keep returning to Halo 5 as my personal go-to title. I found enjoyment with Titanfall and Titanfall 2, but online population issues ruined its online matchmaking. I had a similar experience with Battlefront 1, but I hated the DLC aspect which brought down aspects of its matchmaking. I definitely feel like I wasted my money on Battlefront 2 despite a better approach with the DLC. I enjoyed Destiny for a pretty good period of time, but I stopped playing it when I couldn't buy the Taken King expansion by itself. Activision's perspective on DLC pissed me off and I left Destiny behind. It's also why I haven't invested in Destiny 2 despite what might be a decent game with the most recent Forsaken release. I liked Battlefield 1 after picking up the Revolution version that included all the DLC content, but I didn't care too much to play it solo so I rarely play it. I liked Doom for the campaign, but couldn't get into its multiplayer. I never played much of Far Cry or Overwatch even though I have friends who tell me to join them. One even bought me Overwatch to play with them. I was happy to return to the CoD franchise with the individual sale of Modern Warfare Remastered and I eventually got talked into getting World War II (+ Season Pass) when it was on sale. I find the remastered CoD4 title very fun as it rekindles a past experience in a good way and WWII isn't too shabby either. But I have less than a mild interest in playing Black Ops 4, so I haven't got it and probably won't get it. I dabbled with Fortnite during its Beta, but haven't really had any interest in playing the Battle Royal mode nor one that involves building stuff. Funny, my daughter plus the kids of my friends and family members all seem to primarily play that game - it's pretty ridiculous. I guess it's the primary FPS experience for most new gamers within this era of gaming which I find a bit sad that it's not Halo.