I should have a copy/paste ready because I see this all of the time.
Use the Intel SATA Ports or whatever the Native Chipset is on your particular MOBO. Example the Intel are FULL bandwidth and not shared and connected via DMI.
Example the ASMedia 1061 is PCIe x1 2.0 or <500MB/s shared, so (2) ports = <250MB/s + PCIe switching latency vs Intel SATA3 (2) ports = 1,200MB/s or 600MB/s each.
Now if you're using (1) device on the ASMedia 1061 I would expect faster than 250MB/s but it's a mute point the Intel SATA3 will pummel the ASMedia 1061.