I decided to see exactly what the differences are between the available soulforges. The following is a general guideline that shows the general differences of success percentages for a GM-made ring between the different soulforges. These figures are for a Gargoyle with Legendary Imbuing. These results can be extrapolated for other items:
-------------------HOME--------PUBLIC-------QUEEN'S
1st Imbue--------202.5---------222.0---------227.2
2nd Imbue-------123.6---------136.5---------141.7
3rd Imbue--------73.6----------82.4-----------87.6
4th Imbue--------39.6----------45.4------------50.6
5th Imbue--------14.6----------18.4------------23.6
------------------------------------------------------(21.8 for non-GM item)