USB 3.0 vs eSATA makes no difference; the bottleneck is the drive itself. The fastest mechanical hard disk drives can transfer at slightly higher than SATA I speeds (about 1.5Gbps). But, of course, against USB 2.0, either one is a better choice.
That is, of course, assuming that you are not using SSDs as external storage. That's kind of a waste of an SSD.
Also, for USB 3.0, you require hardware that supports it. If your externals can only use USB 2.0 and eSATA, use eSATA.
(By the way, by "case" I meant "computer case," not "hard drive enclosure")
I'm pretty sure that you can find an eSATA expansion that doesn't need a PCI slot, since it really just channels directly to the SATA port on the mobo. That's a better alternative than what I suggested earlier.
Don't think too hard; it's really not that complicated. It's basically connecting a SATA device externally with a slightly different connector.