It would be a very strange design if an onboard PCI bridge would slow down CPU bound x16 then. It's rather off-topic, but since the question came up, here is what I discuss in a Gearslutz (forum) thread:
The Startech card uses a Pericom Semiconductor PI7C9X113 PCI Express to PCI-X Bridge. This is a good thing, because I had good experience with the PI7C9X111 in another adapter. Both the Startech card and the other adapter allow me to drive RME PCI cards down to 32 samples buffer.
On the other hand I had a bad experience (as in did not work at all) with a PCI adapter card that looks similar to the Startech, but used an Asmedia based chipset. That being said, I think it was more a thing of these cards being cheap (10+ EUR compared to 40+ EUR for the Startech) than a problem of the chipset. Asus/Asrock boards usually use a current revision of the Asmedia ASM1083 chipset, which in the past I tested to be working properly, but older revisions caused trouble for some people. My Z87 Gigabyte board uses a IT8892E.
One drawback of the Startech card is that you absolutely need to use the power-cable, even though there should be enough power from the PCIe bus. My Pericom based adapter even drives two (2) PCI cards from the PCIe bus alone. It does provide an extra power-plug (SATA based), but I don't need to use it for the RME cards.
My PC case offers a single vertical slot opening. This allows me to combine the Startech card with an extender cable and then have a RME card properly installed in the case. You need to be careful with these extender cables, because the quality is not so great. I had one solder pin bent to its neighboring pin, which I noticed before using the cable and then fixed with a soldering iron.
If your old audio card doesn't work then this can be a sign that the card itself has some defect, too. The DSP MADI shown in the image sometimes causes my PC not to boot when it's used with the Startech + extender cable, a AES works without problems. In this case I happen to know that my MADI card had some defects for some time (aka needs repair), so the adapter problems are just a symptom of those card based defects.
My other mentioned Pericom based adapter is this Sintech one (bought via Ebay from China):
They also sell a 5.1/4" slot/external chassis based solution: