What’s the advantage of using T1 over the regular Verizon phone system in an office?

We have an issue of static with the Verizon system in our small office. A different line every time; can't pinpoint when, where or why it will happen. Verizon and our PBX manufacturer just point fingers at each other, w/no solution so far.

Swapped out all of our PBX equipment a while back, so I think it's Verizon. Someone suggested going to a T1 for the phones -- we already have one for data -- to circumvent Verizon. Need to know what the possible risks are. Any help is appreciated. Thanks!