(simplification) PCIEx1 videocard will be 16 times slower in work compared with PCIEx16 videocard.
So dont bother to think about which card will be better.
I suggest you to pick simple and silent videocard (without fans), maybe even low profile card.
Well that is really a simplification, and most of those weak graphics cards aren't powerful enough to utilize x16 anyway so it would be pretty useless to use a x16 slot.
For example, my board has PCI-E x16 2.0, and yet my PCI-E x16 3.0 GPU works just as fast as it would with a twice as fast PCI-E x16 3.0 slot.
Why? Because the GPU can't utilize all of the bandwidth anyway. So when a GPU is weak to begin with (like the GT 610), dropping down from x16 to x1 will not make it perform 16 times worse.