According to a little research, the AF630 blah-blah is actually a GeForce GT630, with 2048 MB of DDR3 RAM. Of the two cards you listed, The GT is much newer (released some time in April of 2011, vs April of 2006 for the Quadro). The Quadro uses GDDR3 RAM (faster clock speeds), but is limited by being old (as far as GPUs go). The GT630 also supports PCIe 2.0, where the Quadro does not.
See the two images below for a comparison of your two cards against others on the market.
Since you said that your motherboard is kind of old, I don't know if it can support the GT630, (and have no way of checking, since your link is broken
To answer your latter question, PCIe 16x has 16 'lanes' for data to travel through, where as standard PCIe has only 1. If given the choice, always put a graphics card in a PCIe x16 slot.
According to benchmarks, the GT630 is much better than the Quadro FX, but the age of your motherboard might cause it to be incompatible with the GT630 (Can't tell for sure, don't know what your motherboard is).