Here is a better image.

The second is more complete and better balanced.

The elaborate lower curve of the second one distracts a bit from the impact of the nice P. on the other hand the first one looks incomplete. Why not compromise and extend the curve of the first one only to just before it crosses itself?

Is the flowery ornateness appropriate to her graphic design style?

Thanks for your comments.

Anthony, Flower ornateness is not particularly her style. I do agree that the ornate curve seems a bit too much.

Vladimir, I will try your suggestion. I am afraid it might look like an infinity sign and not very nice. A little more extension on the inside could be a good solution.

Yes about the infinity sign. Seeing it afresh the one on the left looks fine - but I notice that the legibility of the P will be helped if you delete the middle hairline and make the top gap a bit smaller?

Tried all the suggestions and more but nothing seems like an improvement. So I have decided to go with the left P. Thanks for all your help.

First one is best and creative in view and eye catching on the other hand second's curve is not correct.