I too have a YZ125E (Had it from new) & a YZ250E (In bits but complete, paid $1000)
oldyzman
The 125E should not be peaky. I have 125F's as well & due to porting cahnges were peakier than the E. It's on the pipe or nothing at all.
When my daughter raced I had to put the E motor in the F frame for that reason. She could not "Hold it on" the way the F needed to be ridden but the E motor suited her "Roll on the throttle" style of riding. So much so she ended up 3rd overall in Clubman that year. The E certainly has more low to mid range pull (As much as a 125 can muster) than the F.
I would suspect the barrel you have has had some porting work done.
valleyam
No expert on anything (Except maybe drinking beer, still learning) but have many Yamaha's and know a bit about them, particularily the electrics. Give me a call if you are stuck on something, I may be able to help.
Viper666 0427 334 186