Engine sputters when accelerate fully

I have bought a Suzuki CS50 1987, the previous owner install a performance air filter and exhaust. I took it for a test a short one, I did not full throttle.
When I trying it out today a beautiful day, I was to reach over 15mph, and I start to fully throttle, the engine start to sputter when accelerate between 80% and 100% throttle the engine stall. The engine were half warm, I was wondering if the owner has installed jet needle are too large, when my engine at top end sputters it means lean or rich??

Do I need to focus on needle pin or main jet?

thanks

 

Could be the main jet either too big or too small.
Take it out, tell us the jet size number, carburetter size etc......
Photos help as well

 

Here is my carb, it has been cleaner, the diameter hole is 29 mm, the main jet is 87. I have to test the auto-choke it is function well. Should I down to 85 from 87 main jet?
The needle pin are this correct level?

When I go more than 3/4 of throttle it stalls the engine, when it is nearly 3/4 of throttle it is smooth but when pass the 3/4 it's smoking a bit of white oil out of exhaust and stall the engine quickly.

 

Also, my mate reckon the auto choke by heating thermal from the engine mind not close fully could be why it is sputter too much fuel at high throttle?
I was to wonder if I could replace into a manual choke carb it would be easy to live with it?