Why not use tile instead of mineral wool for sound proofing

Think about what you are hoping for. A 10dB reduction means reducing the sound power by a factor of 10. Dropping the sound power by 60dB therefore means reducing it by a factor of 1 million, or stopping 99.9999%

To put this in context, this is equivalent to building a wall that blocks 100% of the sound, (let's say the wall is 9' tall by 10' wide), and then leaving a 1/8" diameter hole in it.

See also the wikipedia article on sound transmission class, which suggests that typical interior wall construction gives STC 33, and that STC 45 is sufficient for loud speech to be inaudible. STC 45 can be achieved with double layer of 1/2" drywall on each side of the partition, over wood studs with batt insulation in the wall.

Soundproofing as it relates to windows is all about mass -- the denser the materials, the more sound reduction you'll get. PVC is, indeed, typically more dense than the far more lightweight aluminium and so will will resist noise transfer more. However, the amount of surface area made up by the frame is absolutely dwarfed by the glass itself. Any differences in the frame will be massively overshadowed by the properties of the glass, make it a moot point.

PVC/Vinyl windows do a far better job of restricting conductive heat as they are a much better insulator than aluminium. Aluminium is really one of the worst materials to use from an insulation standpoint.

However, PVC/Vinyl will eventually "melt" in a hot environment. Recycled PVC will do so far faster than virgin PVC, but even the latter will eventually sag enough that opening and closing the window will be tricky. Assume maybe 15-20 years.

Aluminium will last indefinitely. That and the price are typically the two big selling points of that material.

In short, neither has a true advantage from a soundproofing perspective (the glass does quite a bit, though) but PVC is a better choice from an insulation standpoint if you are willing to replace the window every 15 years or so. If you don't care about the insulation value and don't want to replace the window, then aluminium is the way to go.