I've seen where some that say component looks better than HDMI. I personally have all my TV's connected via HDMI. I like the cleaner, one cable look.
While the tech was trying to connect you up, did he say there was an issue with the U-verse receiver's HDMI out or the TV had an issue with it's HDMI port? Was the TV's HDMI working on your previous service provider? If so I would think he was having issues with the U-verse receiver. If that's the case and you want HDMI I would ask the box be swapped out with a new one. One of the community managers here can assist you in getting this taken care of.
When it comes to the difference between HDMI and Component cables, there is no difference, as of right now, on our U-verse services. Actually, the way TV is transitioning right now, it does not seem like it will be a difference any time soon. The main reason that you would want to go HDMI with our service is if you have a 3D TV and wish to look at 3D VOD. Component cables do not support that. Other than that, both give optimal resolutions of 1080i, although HDMI can go well beyond that, but our TV service does not broadcast higher than 1080i.
The main benefits of component cables is that there are known issues with HDMI cables. With HDMI, a 3-way handshake process is performed when the two devices start up a connection. So this happens when you turn on the TV, change the channel, and even some of the menu changes. If the 3-way handshake process fails at any point, then usually there is no picture or an odd picture like a pink screen. In our case, our STB displays a warning message stating there was and HDMI error and states to reboot the cable box. This happens very rarely, as with my many years of using HDMI connections, I have only had a problem 3 times with my devices that are connected HDMI, and only 1 time with my STB. But I have had calls where people state it happens every week, and we just transition them to component cables and the issue is resolved.
Also, with HDMI as BeeBee SA stated, the wiring looks better and is easier to handle with the 1 cable connection, and also, with many new TVs, there are a limited number of component connections vs HDMI connections.
Sometimes there may be a picture difference between the HDMI input and Component input, but that is not due to the signal, and can be easily rectified on any TV by simply changing the brightness/contrast/color/and any other simple TV settings.
If you encounter any issues with your service or equipment, I recommend checking out our Troubleshoot & Resolve solutions to help diagnose the issue.
*I am an AT&T employee, and the postings on this site are my own and don't necessarily represent AT&T's position, strategies or opinions.