SATA300 vs. SATA600 compatibility

Hi,

I have a 500GB Seagate Barracuda that comes with a 5 year warrantee. I'm
having problems where various files became corrupted and don't work. I've
exchanged it once. Seagate Tools said it was slow. Maybe I'm doing something
wrong under the assumption that SATA300 and SATA600 are compatible? There
are various PCIe SATA600 adapter cards available.

I bought a PCIe USB3.0 adapter card that now works OK. The first one was
junk.

Given this info, what are the chances that a PCIe SATA600 adapter card will
make the 500GB Seagate Barracuda work flawlessly?

Thanks in advance.