Why is PH3 polar??

You are right to state that electronegative difference between P and H is nearly zero. However, we notice that the dipole moment still cannot be cancelled out each other because of it's trigonal pyramidal shape. So it is slightly polar or nearly non-polar in nature. I guess you are mislead by the bond angle of NH3, which is also 107.
Since N is more electronegative than P, the N-H bonds is more polar than P-H bonds in their molecule. So the bond pair - bond pair repulsions between N-H bonds are much stronger than those in P-H bonds. So N-H bonds repel stronger with each other than P-H bonds. Thus NH3 should have a higher bond angle than PH3.

圖片參考：http://upload.wikimedia.org/wikipedia/commons/thumb/b/b5/Phosphine.png/548px-Phosphine.png

PH3 has a smaller bond angle because the lone pair electron of N (in the 2 nd shell) is more concentrated in a smaller space (less diffused) than that of P (in the 3 rd shell), so there are stronger lone pair- bond pair repulsion in PH3
since stronger lone pair- bond pair repulsion in PH3 ,個下面既PH bond angle就會壓細左。
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the resultant dipole moment of PH3 is nearly zero, but actually is considered as polar. because although P and H are same electronegativity (2.1) but as you can see in the picture, there are lone pair upon P, the lone pair carry partial negative and the P carry partial positive, so that why it is still polar as the dipole moment have not cancel out.

more polar bond --> stronger repulsion between bond pair? sure?

as far as i know, it's related to bonding nature / hybridization / orbitals used in the bond formation.