I know I am well LATE to this forum, but had to voice my opinions.
I feel like the TYPE of each is important, for example there are many cat-girls whom I wouldn't pick over a fox-girl any day of the week, however Omamori Himari's female lead Himari is a Bakeneko (Monster/Demon Cat) and is absolutely stunning with her samurai-style servitude and yet still extremely seductive towards her master with just the right amount of Nyaa~'s.
Meanwhile my preferred type of Fox-Girl only has so very few animated characters whom I would actually go for; Tenko Kuugen, Konohana-Tei girls, Hagoromo Gitsune, to name some of the few, as opposed to the plethora of animated cat-girls. I do however love many Fox-Girls who appear in various un-animated manga such as Yuki from Tamayura Kitsune, who is a fox granted human form by the god whom she serves as a shrine-maiden (Fox-Girls make the best shrine maidens).
Honestly have very little interest in Dog-Girls, of course if you count wolves then Holo the Wise Wolf (Spice and Wolf) is hands down the greatest animal eared girl in history (first animal eared waifu), though her appearance and actions are so fox-like that it irritates me that she is said to be a wolf. However there is one dog-girl I have found in the past year of two that has been deemed waifu material and that is Wereanna from Kamitachi Ni Hirowareta Otoko (at least the manga) as she is fiercely loyal and beautiful, of course her wolf-like feeling helps earn her points.
Similarly there are many Sub-Categories such as cats > big cat - girls, such as tiger girls or what have you that have a strong appeal. In the end it really comes down to individual characters traits for me, but I do admittedly lean towards Fox-Girls (Kitsune), the only outliers that could convince me otherwise are samurai cat-girl Himari and Wise Wolf-girl Holo.
(Unsurprisingly all of my favourite of each are yokai/demons/spirits, which is where I spent my early anime days)