What is the current status of the performance of nVidia vs ATI video cards?

In terms of hardware, I think at this moment ATI is providing more bang for your buck, with many cheap cards outperforming NVIDIA cards of the same value.

However, while ATI's open-source drivers are continuing to improve, I don't think they (nor the binary fglrx driver) compare with NVIDIA's proprietary driver -- yet. If you're using a typical desktop/office machine, you may be okay with a nice ATI card and either set of drivers. However, if you plan on doing any gaming, I think you may have less of a hassle using NVIDIA. So, at this point in time, I'd say an NVIDIA video card may be your best bet purely because of the drivers.

I have an NVIDIA GTS 250 and it's been running without issue, except for a text rendering bug in 10.10 (which is still beta) which has already been fixed in a newer driver.

The scenario has changed in Ubuntu 16.04 ;-)

If you were using the AMD Catalyst (fglrx) driver on older Ubuntu you may wish to avoid upgrading to Ubuntu 16.04.

The ‘Xenial Xerus’ does not support the widely used proprietary graphics driver for AMD/ATI graphics cards.

Instead, Ubuntu "recommends using open source alternatives (radeon and amdgpu)", and say "AMD put a lot of work into the drivers, and we back ported kernel code from Linux 4.5 to provide a better experience."

More details:

• OMG! Ubuntu!: Why Radeon Users May Want to Avoid Ubuntu 16.04 LTS

If you already have an AMD graphics, Don't panic! You will definitely find a lot of workarounds and fixes. But if you are planning to buy a new laptop fully supported by Ubuntu, best bet is to go with nvidia graphics.