Can someone explain what is the difference between hsw vs byt timer implementation?

It looks like hsw uses a generic xtensa timer implementation based on directly reading Xtensa special registers while Byt uses some bits in SHIM layer.

What is the advantage of byt implementation?

Also, the implementation for hsw looks generic enough so that it can be used by other architectures that do not have a shim layer, right?

IIRC in Baytrail we had "external" timer registers available in the SHIM, which weren't affected by frequency changes. it's literally a wall clock. I don't think Haswell had this.

I don't think there is any hard-set rule for the timer implementations, you just select and add support what's best for your hardware.