I'm not 100% sure, but I think the sender is on the output side of the filter. A couple of months ago, I lost all pressure at the gage. I was freaking out as I just replaced the engine last summer. Anyway, as a test I replaced the Fram (I know) filter with another. Pressure came right back up. My conclusion is the Fram filter got dirty and rather than bypass the filter it just shut the flow down. Not going to use a Fram filter again!
I think if you've got a reasonable amount of pressure (13 Lbs at idle sounds okay), then all is good. That is interesting that there is that much difference between the two brands though.