This is a tough one for me. Unlike the case of Tiger and Jack, there is more going for Arnie than just 7>5. To me the biggest difference is that for a period of several years Arnie was rightfully regarded as the best player in the game whereas at no point in his career has Phil been widely considered as the best player in the game for even a single season.
Arnie has 2 POY awards, Phil has none.
Arnie has 4 Vardons, Phil has none.
Just as it is facile to use the 18>14 argument, I think it is equally facile to pick Phil solely on the basis of strength of field, even if we all agreed on what that effect was.
So I am not picking Arnie because of 7>5, I am picking Arnie because:
1) Phil was never considered the best player in the game, while always among the top 5. But Arnie was considered the best player in the game for a period of time.
2) Arnie has the POY(2) and Vardon(4) awards that Phil has never really even gotten close to
3) contra all of that, Phil played in more challenging fields.
4) 7>5 - but this is the least important factor, for me, in Arnie's favor - and if we just look at this metric I think an excellent case can be made that Phil's major victories are more impressive than Arnie's. But as I have said all along majors are not the only factor. Even if everyone agreed wit the proposition that Phil's 5 majors are more impressive than Arnie's 7, there is more to the comparison than just majors and in this case the older guy has more going for him in the comparison than just 7>5 - which I will again point out is NOT the case in the Jack/Tiger comparison, where 8>14 is ALL the Jack people really have.
So for me it is a very close call but I have to go with Arnie by a whisker.