Both types are good, and researching on your own you can find out the physical differences. Seat types, tree differences, different horse fits, fenders, leathers, horns, thigh rolls. Each excel at their own purposes but I imagine you're looking for just a casual saddle.
To me, there are good and bad varieties of each type. I have to sit in them to know. I love some westerns and I love some Australian stock saddles, but I can't ride in others of both types. I find with westerns that they can be too wide for me, and I find that stock saddles are often too constrictive and have the stirrups hung too far forward.
I'd LOVE to find an Australian saddle with the stirrups hung too far forward! But saddles do differ greatly within a style. We have a Circle Y Mojave that my daughter loves in spite of it being to big for her. It is my size (16), but I hate riding in it. But I also have a Martin saddle that is comfortable for me to ride in, although it is supposed to be a 15...and my daughter cannot stand it.
If you want to ride 'on your pockets', a western saddle is better. That is what it was designed to do. If you want a forward seat, the Australian or English saddle is better. The poleys are in a better position to help you stay on than the swell of a western saddle, but the western saddle feels broader and more stable than the Australian - although I've never had a saddle slip. That is just how it feels to my butt and thighs.