Oh wow I was just wondering the same thing. I haven't tested this yet (and even if I did it would be a small sample) but certainly from my limited experience today after getting Ayagasa I only ran into one Stefani, but when I was leading my 7* Ignis I met Stefani a few times (similar use of TP I think but Ii'm just guessing that based on the overall length of time I was using each).
In fact it SEEMS like when I use Ayagasa I encounter less # of princesses overall. Could be just a coincidence so I wasn't going to mention it, but since you did I'll just add that. I seem to remember in some training events in the distant past that it was deemed worse to use the EU4 than it was to use a good 6 in terms of # of encounters, but here we have the added complication of the additional love points we get when using the EU.
After work today I'll do testing with both. We might want to move this conversation to the event thread.