Inkscape's main feature is that it is open source and thus free , I use it for that reason and because a lot of our folks use it but which ever one you are comfortable with should be fine though. I don't know how to set the parameters in Illustrator, maybe someone else will though. Here is the xml that you want to change (from editing your schematic xml file) in case that tells you what to change:
<?xml version="1.0" encoding="utf-8"?>
<svg version="1.1" id="Layer_1" xmlns:xml="http://www.w3.org/XML/1998/namespace"
xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" x="0px" y="0px" width="108px" height="165.6px"
viewBox="0 0 108 165.6" enable-background="new 0 0 108 165.6" xml:space="preserve">
what you want to do is replace the width="108px" and height="165.6px" with the equivelent in in or mm. Then the scale is set without fritzing needing to guess at how many px per inch is being used. It isn't vital because Fritzing appears to be guessing correctly as the part is properly scaled, only Inkscape is having problems. It looks like you have an older illustrator that is using 72dpi as px as changing the height / width in Inkscape to height 2.3in width 1.5in (calculated by dividing the px values by 72) looks to fix up the scaling in Inkscape. The main issue is that terminals defined as a path don't seem to work, so replacing them with either a polygon (such as connector12terminal) or a rectangle will fix that. Setting fill to none with a stroke width set to make an outline around which ever polygon is making the board shape should fix the silkscreen problem (not that I know how to do that in Inkscape let alone Illustrator though ) one of our more experienced board makers may know how to do that though. In Inkscape the hole size is set by stroke width and hole diameter. The current values (in Inkscape) are diameter .065in increasing that to .068 will make the hole .038, but it (at least in Inkscape) will also move the x y coords a bit and misalign the board. I usually use the xml editor to figure out what the new radius should be and manually change that (which keeps the x/y coords constant in Inkscape).
edit: A bit of experimenting in the pcb svg indicates that setting fill=none in the polygons and path in group silkscreen XMLID_1_ g6 and g10 and path13 fixes up the silkscreen problem.