Almost impossible to answer, unfortunately. The SATA standards for "normal" SATA do not include a few features that are required in a true eSATA port. Among these are support for longer data cables (using stronger signals) and support for Hot Swapping. Some mobo makers (that is, the chips they use to provide the SATA mobo "Standard" ports) actually have those eSATA extra features included, and some have a few of them but not all, and some have no extra features. When you use the adapter cable alone, you rely entirely on the mobo chips to provide some features that eSATA MAY need to work, but you can't tell whether they are there or not. IF you want to be absolutely sure, you need a true eSATA controller, which that PCI-E board will provide.
You should know, however, that it is common for some eSATA features to be in "Standard" SATA mobo ports. Even if they are missing, sometimes it does not matter. For example, if your cable to the external drive is not too long, the signals may be quite good enough to work reliably even if they are not extra-boosted to eSATA standards. If you do not have Hot Swap support it does not matter if you never try to use that capability, anyway. So many people will try the free (or at least, cheap) option of the adapter cable. If it fails, you wasted very little money finding out you need something better. Be aware, however, that you should NOT try "Hot Swapping" in this case. That is, do not simply disconnect or connect the external drive while the computer is in use. You may corrupt data on the external drive doing that, and that could ruin ALL the data on the drive.
SATA port - Design to use internal, relative short distant cable.
eSATA - it's a SATA bus with better shielding to prevent RFI/EMI interference up to 2.0M
eSATA/SATA port performance is base on its chip set and the bus connection to IHC
If the motherboard SATA chipset connects to IHC via 1x lanes then it has the same bandwidth as other PCI express 1x lane eSATA/SATA adapter
Look at the MB architecture you can pretty much tells the performance of the particular eSATA/SATA port.
If you connect A SINGLE drive to this eSATA port using bracket or PCI E x1 lane, there should be no different between the two, cuz a 7200RPM SATA HDD CAN NOT overflow the SATAI, SATAII bus speed any way.
The bracket is not reliable, as the voltage signal levels for eSata are not the same as for Sata. Just changing the socket it begging for problems.
Also, take a look at my personal preference for this, the bare-drive bay. If you have one external drive an eSata enclosure is reasonable, but I have a box of ten drives that I swap in and out, so this method works much better for me.