Originally Posted by sosidge
Sounds like it might be related to voltage drop on power.
How are your batteries? If they are old or poor quality they may be struggling to give enough voltage when the extra power of the brushless comes in.
Also give all your wiring a good going over to check for damage and make sure the antenna runs up through the tube.
I had a very similar problem when I put a new ESC in my ride too. It was a voltage drop. I was running NiMh 4200's and every time I got on the throttle the car would pull right and cut out for 10 to 20 seconds.
Turned out there was a setting on the ESC for either NiMh or lipo and it was set as default to lipo. This caused the ESC to think it had more power available and when it drew the power the problem occurred.
After I got some help from the guys at the track and changed the setting (20 seconds to fix) I haven't had this issue since.
Hope it helps.