You should always check BOTH.
TV and PS3 should show up on that site, all you need is your PS3 or TV model number. It takes you to the model page, and lists Software/Firmware upgrades.
With Firmware, you do have to actually setup your TV or PS3 again, just like you had to do when you first purchased the units.
So, before any updates, it's best to write down all your present settings, then perform the updates, and access each unit connected, THEN set your settings. The reason why is EACH INPUT remembers the settings in the menu.
Especially the 3D settings on your PS3 input.
Sony usually provides details on what each upgrade does....example is it -- corrects audio issues or 3D issues, or allows a certain DVD to play properly. I always read them to see if they will correct a problem or not. If not, then I usually avoid the upgrade.
And when you do upgrade, the upgrade does not take effect until the unit is completely powered down, unplugged for one minute, then restarted.
There are minor tricks to getting the update to load, so keep that in mind too...
TVs and PS3s are more computer-like nowadays, so treat your updates like you are installing them on a computer. You usually have to shut it down and restart it for the updates to actually load.