Oxford college choice and funding

[Manana]

So I am wondering whether I should make an open application or specify a college. My main issue is funding. From what I've seen so far, a very small number of college scholarships in the humanities require specifying a college.  Most of them only mention that if you secure the scholarship you might be transferred to the awarding college.

So my question is- does it matter, funding-wise, which college I specify as a first choice? Say if I see that a certain college offers a relatively large number of scholarships, do I gain anything by specifying this college in my application?