I can't say that Quinacridone Magenta is better. It's just different.
Which colour is better really depends on the context. It could depend on the subject that you paint. For example when you paint botanical art, flowers, you may need to use very specific colours. Or when you run out of paint and can only use the other red, that red becomes the best colour you have because that's the only colour have. Different artists also have different preferences so a colour that I like may not be a colour that you like.
One important thing to note about Alizarin Crimson is there are two versions. There's the normal Alizarin Crimson (PR83) and Permanent Alizarin Crimson. The first is fugitive and can fade when exposed to light for prolonged periods. The Permanent version is the lightfast version, but it's made of three pigments, namely PR 177, PV 19, PR 149. When mixing, I don't find the three pigments having much negative effect. That said, most artists would probably choose single pigment paints.
On paper, Permanent Alizarin Crimson appears to be more red. And Quinacridone Magenta is magenta, of course.
These are the oranges from mixing with Lemon Yellow, New Gamboge and Yellow Ochre. The top row is Quinacridone Magenta. When it comes to mixing orange, Permanent Alizarin Crimson has slight advantage because it's a warmer red compared to Quinacridone Magenta, and because of that the oranges are slightly more vibrant.
I like to use cool reds to mix with Phthalo Green to get dark shades. For some reason, I think I used the wrong Phthalo Green in this picture above. Looks like a Turquoise instead. But the same principle still applies. When you mix cool reds with cool greens or cool blues, you can get very dark shades.
When mixing purples and violates, Quinacridone Magenta has the slight advantage. The violets and purples look slightly more vibrant compared to the mixes with Permanent Alizarin Crimson.
You can mixed rather dark blacks with the three primary colours. When you use warm primaries for mixing, you can get a warmer black and sometimes brown. And with cool primaries, you get cool blacks.
So while Quinacridone Magenta and Permanent Alizarin Crimson look quite different straight from the tube, the difference with mixing with other colours isn't that significant. Depending on the subjects that you paint, you may choose one over the other.
Permament Alizarin Crimson is an interesting colour. I'l certainly going to explore the three pigments that make up this paint in a future video.