This is a challenging question which I've answered before. Here's my copy and paste answer:
*Graphics
Gears of War has an obvious advantage in the visuals department as its built on the newer, more intensive, Unreal Engine 3.5. Halo 3 uses a proprietary Bungie-built engine known fittingly as "the Halo 3 engine." Gears of War is highlighted by finite details like slight environmental deformation, artfully sculpted lighting and meticulously designed character models. Halo 3, on the other hand, feels like it was built on a crumbling engine that, while it does produce some impressive scenery, just can't quite compete with Gears of War when it comes to awe-inspiring settings for the chaotic action. There's something to be said for the fact that Halo 3 can push four-players through the campaign as opposed to Gear 1's two-player support, and Halo 3's replay editor is very impressive, but that doesn't stop Gears of War from being the better looking game overall.
*Sound
Both Halo 3 and Gears of War feature splendid original scores that compliment the feel of each series, as well as what's going on in the given scene, extremely well. But which game's orchestral arrangement got our heart pumping the fastest.
Gears of War had acceptable music. On the flipside of the coin, the voice acting for Marcus, Dom, Cole and Baird was pretty terrible. It was cheesy and poorly acted.
Every Xbox owner knows the Halo theme. Every battle has perfectly cued sections where the music chimes in to sell the importance of the Chief's actions.
Much like Gears of War, the voice acting is cheesy in parts, but Halo 3's will never quite make you slap your forehead in disgust. The sound effects are just as iconic as anything in Gears, with the battle rifle and assault rifle both returning to prominence.
Halo 3 wins here hands down. It is without question, the greatest musical arrangement that I've heard used in a videogame. It works so well with the feel of the Halo universe and what you're physically doing in the game.
*Story
Both Halo 3 and Gears of War provide serviceable storylines that serve different purposes for their respective series.
There's far more going on in any one scene and the struggle that the main characters go through hits on a personal note. Gears presents us with new characters that, rather than becoming integral parts of the storyline that we -- as the player -- can't yet connect with, are used to drive the darker parts of the plot.
Halo 3 was a bit different than Gears in that it needed to present an acceptable note of finality to the trilogy of Master Chief. He was as close as the Xbox ever got to having a mascot so people needed a fitting end to his heroic tale. Halo 3 serviced our beloved icon well, but it felt a bit too traditional; like it was following some sort of laid out path. It even went the painfully unoriginal route of sending the player back to another Halo planet. The odd love interest between the Chief and Cortana is a little strange, but it worked on some levels.
Neither Gears of War nor Halo 3 will be remembered as spectacularly written storylines or incredible depth of character, but Gears of War does present the more engrossing campaign. The connection that you'll feel to Dom's struggle to find his wife, Maria, is much stronger than anything in Halo 3. Similarly, the new plot developments, use of new characters and the mention of a few hanging strands of story from the first game, are simply more fun than venturing back to a planet that we detonated back in 2001.
*Gameplay
There's no question that these games have differences, but what unites them is actually greater than what divides them. Both are shooters, both have strong main characters, both vehicular portions and both are considered the best at what they do. But which is better.
Gears of War hinges on its ability to allow gamers to move fluidly through the environment and stop and pop up behind cover. The mechanics are fluid.
Halo 3 stayed even more on the beaten path than Gears of War; deviating little from what had been laid in front of it by the first two games. It gave the Chief the use of equipment in battle and tossed in some new vehicles and weapons, but for the most part Halo 3 felt little different.
Where Halo 3 made its mark was in the size of the incursions. Every battle was bigger and more compelling than what was in the prior two releases. It was thanks to the Xbox 360 technology that we were afforded such an expanded experience, but Halo 3 did a fine job of not losing its focus and sticking to what people know and love about the series. It still has the best FPS controls on a console which then meld perfectly into the splendid vehicular controls for which the Halo series is known.
Halo 3 is a better overall experience than what Gears of War tries to present. Everything in Gears of War is very good, but none of it delivers the overall fun factor of the more focused and centralized experience of Halo 3. Halo 3 may not span the same array of gameplay variants as Gears, but its classic first-person gameplay cannot be beat by anything else in the genre.
*Feature Set
Gears of War and Halo 3 will be spinning in people's disc drives for months to come because they both have an impressive list of features. In fact, some might even say an astonishing list of features.
Being the last game in the heralded Halo series, Halo 3 needed to pull out all the stops in some regard. The game's feature set does exactly that. On top of the more traditional four-player cooperative campaign and bevy of multiplayer variants and modes, players will also find two "outside of the box" newcomers. Forge mode lets players put their own creative touch on any of the game's maps. It isn't quite a map creator, but it's close. Next up is the video editor which allows you to snap screens and video clips of either single or multiplayer action and upload it to the Bungie website or just hand it off to another friend. Toss in the highly underrated meta-scoring and skulls and Halo 3 comes out on top of Gears of War.
*Multiplayer
For as much as people enjoy the solo play afforded by both Gears and Halo, it's the multiplayer that delivers the most staying power. Both Gears and Halo 3 pack some great multiplayer offerings. Both have fifteen maps currently available and a wide assortment of modes. Gears of War offers fewer varieties than Halo 3, but the overall fun that you'll have is comparable. The main thing that Halo 3 has over Gears of War is the fact that there's a larger variety for the number of players and environment types. Because Halo 3 offers up to 16 players and anywhere in between, while Gears is always capped at 10, regardless of the map, Halo 3 feels more different from match to match.
Aside from competitive multiplayer, both games also have co-op play. Gears of War has a two-player co-op campaign mode. The two-player campaign doesn't pack the wow factor of the original. Halo 3 is more traditional with its four-player co-op campaign that is fun, but not earth shattering.
There are two main areas where Halo 3 takes the fuel from Gears of War 1's flame: community support and network code. To start, Bungie.net is the future of triple-A community support. Bungie is able to constantly update playlists and game modes as well as highlighting awesome user created videos and game variants. It is the pinnacle of developer support and is something that should be aspired to. On the flipside, Gears of War does have a cool photo mode.The second point, that of network code, isn't so much a discussion as it is a failure on the part of Gears of War. Since launch there are rampant reports of people not being able to find games and experiencing bad lag when in a game.
*Overall
Halo 3 is one hell of an achievement. It presents players with everything they could want from the final chapter of a first-person shooter and it has the feature set to match. Gears of War is a technical achievement and has a better story than Halo 3, but its other features are where it falls slightly short. Both are great games, but for the best on the system, look no further than Bungie's Halo 3.
Halo 3 is clearly better than Gears. Obviously, Gears has better graphics, but that's it. The gameplay in Gears is problematic, especially, when going into cover every 2 seconds by accident. When playing online, Gears lags. I never have that problem with Halo 3.
Hope this helped.