It really depends on the cooling setup and how much work the PSU fan has to do.
I would need full system specs as well as a description of your cooling setup before I could say anything about that.
If your PSU is top mount, that means all the heat from the PSU goes into the PSU and gets blown out the back of it by the PSU fans. That can potentially be a lot of heat internal to the PSU on a constant basis. Keep in mind that this is in addition to the heat that is normally inside the PSU from its general workings.
I don't know your situation, but I will pretend for the sake of argument that you are using the whole 850w and at 100% load it is 82% efficient. That would mean you were taking ~1037 from the wall. The extra ~187 would turn into heat internal to the PSU.
Add to that 187 with all the heat your graphics card makes, all the heat your CPU makes, and so on (these fans disperse heat, not remove it, so it is still internal to the PC until the PSU can suck it out.
With no fans, the processor and GPU would easily surpass 120c each which is north of 200 degrees Fahrenheit.
The point is, if your PSU is top mounted and it is doing all the work to pull all this heat out, the fan could be forced to work at max all the time to try and keep up. If that happens, the PSU fan will be very loud.
On the other hand, if you have a few systems around that can work just fine on a 350w the heat they throw off inside would be much less and at 82% efficiency at 100% load (assumed) that would be ~427 from the wall and only about 75w (vs previous 187F) that is generated by the PSU itself.
The fans on the 350w could theoretically work a lot less to get rid of the much less potential heat generated.
I hope that gives you a decent idea of the dynamics in play here.
If you want me to give you better info than that I can't do it without knowing the specifics of your situation.
Anyway, if you really are maxing the fan on a top mounted Corsair TX850 then I would suggest getting a different case with a bottom mount PSU setup and fans on the top that draw the heat upwards and out. That would greatly reduce the stress on the PSU fans and probably allow it to work much more quietly.
It is also possible that the PSU fan is flawed somehow which could cause it to be more loud than usual as well. Again, I can't really know this.