OK, some words about noise, a few days late but better than never. Condenser mics have self-noise. No, this isn't phantom power noise, nor is it a defect (unless it's an unreasonable amount). The self-noise of a dynamic mic is much lower because it doesn't have active electronics, so there is just a bit of thermal noise, probably at a level 10 to 20dB below your AT3035.
However, there is no reason at all to use 60dB of gain with an AT3035. That mic is around 20dB more sensitive than your Senn dynamic. Therefore, your gain setting should be about 20dB lower.
The AT is not magically picking up every sound that the Senn can't hear, unless these noises are outside the frequency response of the Senn. But high frequencies don't travel through walls very well, so I doubt this is the case. If you apply enough gain to the Senn to match the level of the AT, I bet you hear the dog too.
But people tend not to treat more sensitive mics that way; instead of normalizing gain, they back away from the mic or sing quietly. It's all about signal to noise, and if you sing 1' from the AT, but 1" from the Senn, the Senn is getting a much higher signal (your voice) to noise (the dog) ratio than you're giving the AT. That concept also applies to the self-noise of the mic. That concept also applies to your room response.
Now, the proximity effect between the two mics probably is different. That is a function of many things; polar pattern, diaphragm size, case, etc. But the correct way to set gain is to experiment with mic placement, especially distance, until you get the tone you want. Then you set the gain on your preamp to the correct level. This might be an iterative process, as backing away from the mic will drop level, etc.
Another thing to be very aware of is how the mic's sensitivity and response affects your performance. Some people get their first condenser and start singing or playing ppp because they can, the mic will pick it up. But that doesn't mean you should, unless you are recording a whisper track or something.
Again, as a starting point, turn down your pre's gain 20dB from your mark for the Senn, then try and see how you like the AT.