Is it better to have a poor top layer copper pour or no copper at all?
In general, I would say keep the top-side pour; it certainly does no harm, and it has some secondary benefits, such as less etching required and less thermal stress on the board during reflow.

You do still need to pay attention to current loops and place the vias appropriately, not just scattering them about randomly. Since the FT232R is the only active chip on the board, focus on its outputs. There are two LEDs that are powered by VUSB, and a few outputs associated with the serial port that are powered by VCC. Where do the currents flow when any of these outputs change state? Try to keep the paths as short and direct as possible.

Note in particular, the ground path for the USB connector in your non-pour example. It has to go down, cross below the chip, then come up on the right before it gets to the ground pins on the top of the chip. The top-side pour shortens this considerably. In either case, it would help if you adjusted the vias near pin 1 of the chip so that the bottom pour is continuous there.

One side point about your design: Try to avoid having three etches come together at an acute angle, like you have on your Vcc trace. Make that a right-angle tee connection.