Hmm your computer is not so powerful indeed.
However, the CPU power requirements of P3Dv4 are quite similar to P3Dv3. I would however be a bit more concerned about the memory usage (both RAM and video memory), which is a bit higher in v4 if I'm note mistaken.
Sorry, I understand we're a bit off-topic here, but did you have the v4 installed, and then reverted back to v3 ?
EDIT: that being said, if the v3 runs well on your computer, then there's no need to go to v4 and I'm not trying to convince you to do so (just to clarify

)
I just wanted to understand the reasons and what you went through, just to see if anything could be done to help.
P3Dv3 is still awesome, and let's not forget it's the last iteration of P3D that accepts the FS9 aircrafts.