Day in and day out this forum is riddled with threads concerning dedicated servers. You could safely say that all of them stem from someone having experienced lag while playing Gears of War 3's multi-player, and it's even safer to say that they will be about one of two things: The player was gibbed by a Sawed-Off past it's range or their gun damage was inconsistent.
These threads usually consist of the OP stating that this is definite proof that they are not playing on a dedicated server, and that is not case. The only conclusion I can reach towards posts like this is that the OP does not understand what a dedicated server does and how their connection to these servers work. I will attempt to explain how dedicated servers work and how you still can have latency issues when playing on them.
Your Personal Connection
To preface my section on dedicated servers, I want to use this opportunity to help players who may have moderate or strict NAT's. This doesn't affect latency but hinders your ability to connect to other players. I'm not sure if a strict or moderate NAT can hurt your search options when trying to find a dedicated server, but it's better to be safe than sorry. To guarantee that you can connect indiscriminately, your NAT type must be open.
The first step is to give your Xbox a remote IP address on your router that will not be over-run by another device. I personally use a Linksys router which grants me 50 IP addresses between 192.168.1.101 and 192.168.1.150. Different router brands are going to use different default IP addresses but the idea is the same. Give your Xbox an address in a high number - at least past 15. This will ensure that any other device in your home won't be given this address by default and override your Xbox.
To manually set up your Xbox's IP address you must go to the Network Settings on your Xbox and then Configure Network. Note your Subnet Mask and Gateway because you will need to re-input these yourself. Now go to the IP settings, change it to manual and put in the information required.
Now that your IP address is set, the next step is port range forwarding. There should be a section for gaming in your router settings. Go to it and look for a sub-section called port range forwarding or port forwarding. Microsoft says that the ports required are 88 under the UDP protocol and 3074 under both TCP and UDP protocol. Input these port numbers and assign them to your Xbox's IP address.
Another option is to enable DMZ on your Xbox's IP address if your router allows you.
Edit: These were solutions that worked for me but if you need more details and other fixes for a strict or moderate NAT you can look here: http://support.microsoft.com/kb/979000 (Provided by: Doc Holliday v2)
Edit: As an example, here is what port forwarding and enabling DMZ would look like on a Linksys router - along with my IP address setting on my Xbox: Settings.jpg
Now that your router settings are in shape we can talk about dedicated servers. A dedicated server is a purpose-built computer that can read and transmit data to players faster than a peer 2 peer network. They are most common in games that allow a vast amount of players in one room - think MAG or World of Warcraft for very large numbers. The servers have an upstream bandwidth built to handle the players way more efficiently than the average broadband connection can. This allows a lower ping and an overall better experience for the player.
However, they aren't perfect. The servers are set up in different regions and when you connect to a game it will attempt to connect you to a server that is closest to you, giving you the best connection possible. Sometimes you may be connected to a server that is outside of your region. I, for example, live in South Carolina. If I connect to a server that is far west or north, I have the possibility of having a high ping compared to the other players in the game.
If my ping is high it will cause discrepancies in my experience. We'll use the example of the Sawed-Off gibbing beyond it's range. The fact is that the Sawed-Off isn't gibbing beyond it's range, latency is causing me to view it as such. For those who play Call of Duty, we all have the experience of "ghost bullets". You run behind cover and somehow an enemy still kills you. If you look at the killcam, you notice that in their view you were not behind cover. This is caused by latency and it's the same effect that you experience with the Sawed-Off seeming to gib beyond range.
The mistake I often see is that players expect a dedicated server to provide zero latency. The fact is when you are connecting to a server there will always be latency. It cannot be avoided. Whether your ping is 1ms or 100ms, data takes time to travel. We all have to accept that sometimes we may connect to servers outside of our immediate region and experience a higher latency than other players. We also have to accept that even when the servers are down that Gears of War 3's network coding is leaps and bounds above Gears of War and Gears of War 2. When our games our sometimes peer 2 peer the connections are way better than they were in the previous Gears of War titles. Epic Games put forth a fantastic effort in making Gears of War 3 the best multi-player experience in the franchise and should receive due credit.
If you took the time to read this post, thank you, and feel free to ask questions.