I personally like the Intel integrated graphics over either of them.
As mentioned numerous times, you'll get half of the folks saying nvidia and the other half saying ati. There's really no better brand/make... all of them got their own set of quirks. If you're seeking to purchase a video card, you'll have to let us know of how much yer going to spend and what do you look for. There are numerous aspects to video card and people have opinions regarding the quality or aspect of a product.
NVIDIA's GeForce 7 series is their latest offering. You'll find a lot of companies making cards using these chips. The drivers can be downloaded from NVIDIA's site and can be unlocked for overclocking options. Its control interface is integrated with the driver's Display Properties applet in a tree-style structure. However, the drawback to this is having to fumble around the Display Properties, clicking on tabs after tabs and navigating through the interface structure.
ATI's X1000 series is their latest offering. Like their competitor, you'll find some companies making cards using these chips. The drivers also can be downloaded from ATI's site. Their Catalyst drivers are numbered systematically in an easy-to-remember format so looking up past drivers is no problem. Another aspect of their Catalyst drivers is their use of the .NET framework for their control interface. Their Catalyst Control Center will not run without a .NET Framework installed so if you do not have this, it will not run. The CCC also features some simple preview panes that helps new users in seeing what they will be getting when they change an option. The CCC is also a stand alone application that is completely separate from the driver package itself. In other words, the drivers can be installed by itself and the defaults applied/used. But accessing and setting options for the drivers require CCC or a 3rd party application to do that. On the other hand, accessing these options to set them is straightforward and more direct.
In the multi-card department, the differences is more pronounced, in that they are so different that any remote chance of compatibility is impossible. On one hand you have SLI, NVIDIA"s offering where you simply add another card, hook up the SLI dongle, fire up the system, and enable the SLI option in the drivers. SLI also offers dual PCI Express x16 operations in nForce4 X16 motherboards. However, there is no documented evidence to show that there's an improvement in performance with dual x16 than dual x8 (normal SLI).
On the other corner, ATI has a similar idea: multi-card. However, their concept is vastly different where you require a Master Card to help drive the multi-card setup, and a regular card that will act as a 'slave'. The Master Card, if I am not mistaken, will handle the reception of data from the slave card, processing that data, and output the final rendered image onto the display device. This means in order to upgrade to a multi-card setup that most would either have planned this out from the very start (ie, get the Master Card first), or must find a Master Card in order to complete their multi-card setup.
"I can only show you the door. You have to walk through it." You're going to have to decide on yer own which one is suitable for ya. It'll be part trial-and-error and part experiences. Pick one and move on.