External SSD vs. Internal standard HD for speed?

Using an SSD in a USB 3.0 enclosure is totally possible, but it carries some pretty hefty disadvantages that make it rather unsuitable for what you're wanting to do:

• TRIM does not work over USB, so an SSD will slow down over time and will wear faster. Also NCQ is not supported, which may slow down reads.
• All USB data storage devices are treated as removable by Windows, so you do not get read/write caching and buffering the way you do for internal drives.
• USB is a shared bus, so the 5GBits/sec speed is shared amongst all other USB connected devices. SATA is 6GBits/sec per port.
• USB uses PIO for data transfers whereas SATA uses DMA. That means your main CPU has to do all the work of moving the data across the bus. A constant, sustained load can slow your whole computer down.
• *Installing* some applications to a USB device can often turn that device into a system dependency (meaning Windows might throw errors or display other odd behavior if the device is not present) -- even if you aren't using that application.
• Some applications won't even let you install them to a USB drive.

Those are just the disadvantages I could think of. If you can live with these disadvantages, then by all means go for it. It will (mostly) work fine. However, if I were you, I'd swap out the internal HDD for the SSD and put the internal drive into the enclosure instead. Note that you'd have to reinstall Windows this way, because Windows will not boot from a USB drive.

In theory it would not work:

• Internal SATA speed is likely to be 6 Gbps, and USB 3.0 is slower than that.
• external USB enclosure is likely to introduce further delays (SATA to USB, then USB to memory) as well as limiting protocol capabilities (e.g. by default the USB drive won't have write back cache, what Windows calls optimize for speed, but write through or optimize for fast removal. At a lower level you lose SMART and, I think, write queue optimization).

In practice, you might get better performance in sustained reads, when the SSD overtakes the mechanical disk cache capability. The mechanic is not always capable of keeping up with the SATA interface, and 6 Gbps is only the maximum talking speed between electronics: the platter may have been left behind.

Run a disk read speed test with large data blocks and see. Values below 4-5 Gbps might indicate a SSD would do better.

On the other hand this is only true if your game does read lots of sequential data. Random reads are probably best left to the internal disk.