I've owned both, plus two 100-400mm. I've just picked up another 150-500mm for casual zoo style shooting in the UK. In order I'd go 100-300mm 4.0, 150-500mm, 100-400mm, but that is just based on the quality of images I got from each, before adding in any further criteria.
The 150-500mm OS is fairly large and heavy and very noticeable, but so is the 100-300mm. The latter needs a monopod to get the A1 image quality it is capable of unless you are very steady. It takes a 1.4x very well too, as Tony says.
I used mine around 80% like that, which is why I finally sold it for the 100-400mm. That was a disappointment, both copies where, but then the 100-300mm is one of the best zoom you can buy while the 100-400mm is just a long zoom that does most thing pretty well.
The 150-500mm OS is a better all rounder If you take weight and size out of the decision, but if you don't need 500mm, and 420mm with a tcon on the 100-300mm is still long, then go for the 100-300mm. If you need flexibility in a fairly lightweight package and decent IQ then stick the Canon you already have.
Not sure the 150-500mm or 100-300mm are that suited to a woman shooter, but depends on build and strength. They are both heavy to be swinging around chasing planes. I know the 100-400mm is pretty popular for that stuff. A decent tripod and ballhead or gimbal will sort things.