Hi Steve,
As the Wiki says "You can be confident that all of the current Macs come with a video card that is compatible with ArchiCAD." One of the many reasons that Apple products are great is that Apple delivers the entire package - so it just works.
That said, your card is kind of ancient. For a question like this, we need to know the model number of your Mac Pro and/or the year. Apple Menu > About this Mac then click More Info to get to the System Report. For example, my Early 2008 Mac Pro has model number 3,1.
I upgraded my Mac Pro to the Radeon HD 5770 for $249 via Apple here:
http://store.apple.com/us/product/MC742ZM/A?fnode=MTY1NDA5OQ
last year and have been completely satisfied. One of the reasons, besides performance, for my upgrade was to get a mini displayport so that I could use the 27" Apple LED display. I've still got my old monitor plugged into the DVI port.
This card has excellent performance and supports OpenCL for the Apple Pro apps that use the graphics card chip accelerator.
There is also a 5870, but I don't know that the extra $200 buys you anything for ArchiCAD: peak performance on games might be better, but it consumes a whole lot more power and these benchmarks don't make a convincing argument for the extra cost:
http://www.barefeats.com/wst10g7.html
Apple's page says that the 5770 is for Mid 2010 Mac Pro's and later - but you can read in the Q/A and on various sites that the card in fact works for old Mac Pros from 2006 onwards.
If your Mac Pro is indeed that old (pre 2008) you might also consider purchasing a SSD for your boot drive if you want to up your performance.
http://eshop.macsales.com/shop/SSD/OWC/
On the other hand, if your Mac Pro is 2006/2007 era - your money might be better spent on a new quad-core iMac which will have much faster memory and processors/etc...and the kernel will run at 64 bit...
Cheers,
Karl
One of the forum moderators
AC 28 USA and earlier • macOS Sequoia 15.2, MacBook Pro M2 Max 12CPU/30GPU cores, 32GB