as i said before... both the 2020 and 2035 use a cardioid pickup pattern so will be similar in that they pick up sound only in one zone while ignoring sound from zones outside this pickup pattern. ideally correct placement of the mic will take care of (most) of your possible audio interferences and not having sounds in your mic pickup zone is going to result in less problems.
you want the mic 3-4 inches from your mouth with a pop filtr, not 2-3 feet away sitting on your desk. use a microphone stand. the mic should be much closer to you than any other sources of noise. many people make the mistake of buying a sensitive microphone then putting it on their desk and complaining it picks up everything (its doing its job).
if you absolutely must do this then there are programs which can edit out such things on the fly. or if you produce videos you can remove such things post production (although not having them to begin with is easier)
the 2035 will have less static and self noise though is also more sensitive and can pick up quieter sounds. this means that potentially the 2035 might capture things the at2020 may not but also has higher quality sound to it as well. with that said you can control much of what is picked up (within reason) by the mic sliders within windows as well as the noise cancellation features in the enhancements tab.
since the 2035 is more sensitive it will pick up things like your keyboard and fans more readily than the 2020 however proper placement of the mic and other components can solve much of this. the 2020 might not pick up as much however will be a little more noisy from self-noise. again, you can affect what gets picked up via volume, gain and enhancements as well.
the fact that one is xlr and one is usb has no bearing on the above other than usb mics tend to have more electrical self noise. the at2020 is available in xlr and usb.