Khan,
A CdP is required to enter your bike into Iran.
Assuming your bike is USA-registered, it would be difficult if not impossible
to enter Iran using your PAK passport riding with a USA-registered vehicle.

As Mehmet says above:
" For Iran, it's better you check on net which passport will give you more official advantage.(Ministry of External Affairs).But ı'm sure Pakistan passport will have more advantage for friendships."

But it's actually a "worse"/ more complicated situation. Iran Ministry will not
issue personal visa to USA-passport holder unless that person is part of an "organized" group or tour arranged through an approved Iran-based travel agent on a pre-approved itinerary. Even if you can afford time & money to make these arrangements, such visa approvals for USA-passport holders also depend a lot on current political climate; very unlikely in current climate.

That leaves your PAK passport as only likely option to enter Iran; and as Mehmet says, you need to find out exact procedure for Iran Ministry to approve visa for PK-passport holder.

That means--in your circumstances--if you are intend to enter & travel inside Iran, the only scenario that might work is:
1) you get Iran visa to enter on your PK passport;
2) you ride USA-registered bike to Turkey-Iran border or nearby city, e.g.
Van, Turkey.
3) you find & leave USA-registered bike in some secure storage in Turkey;
4) you enter Iran and travel inside Iran by alternate public transporation, e.g. bus, taxi or train; returning to wherever you left USA-registered bike.
5) I don't know all the alternate transportation mode details, but I'm quite sure you can also fly or train from Van, Turkey into Iran and return to Turkey;
see, e.g., Turkish Airlines - TK - International Home Page, and Trains Turkey <&mdash;> Iran.