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.
Manufacturing a board, from the customers point of view, is no different no matter what you draw, unless you add excessive numbers of holes to the board. It is much more involved to make a 4 or 6 layer board than a 2 layer board, and the cost and time will be greater. Multilayer boards allow a ground plane and power planes to be used. Once you settle the manufacturing (number of layers, layer stackup, minimum space and trace width, maximum hole density, 'via' technology and minimum size, minimum annular ring, etc.) the cost will not vary much.
Assuming you have a two layer PCB you don't really have the option in most cases of a complete ground plane, because otherwise you would have to lay out your circuit as a single layer (excepting only ground). So your options are pouring or not pouring.
If all or most of your parts are on the 'top', you can often pour a ground on the bottom that is mostly integral. If you care about EMI it's better not to have high speed signals crossing a break in the ground pour or ground plane (you can split planes). You may also choose to pour on the top (where the parts are). In circuits where there is mostly one ground and one supply, it may make sense to pour a ground on the bottom and a supply on top. The benefits of the latter in particular are not so great so you may want to make sure you leave a generous clearance so the yield is not unduly adversely affected. In other words, if the PCB maker says they can do 6 mil clearance, use 15 or 20 mils for the pour clearance, not 6 mils.
The distinction between a 'plane' and a 'pour' on a multilayer (4 or more layers) board is partly the way they are drawn- a plane is drawn in the negative and you may split it (for example to provide a second ground for galvanically isolated parts) whereas a pour is put overtop of conventionally (positive) drawn traces and pads and connected to a net. Either can provide connectivity, so you can eliminate any traces that were there providing connectivity. If you neglect removing those traces you can muck up the thermal reliefs a bit but it should still work.
Either eliminate dead copper (unconnected islands) in the pours or stitch it to connected sections with vias and short traces. In this way you can get a mostly integral ground layer and improve the power distribution at no additional cost.
Best Answer
They are called stitching vias and are used for what you want: -
To avoid EMC problems you may need to have many stitching vias but, without an idea of what your PCB does or what EMC specifications you wish to comply with, it's anyone's guess as to how dense the stitching vias need to be.
It might be as simple as doing something like this: -
I've added red boxes around what look to me like stitching vias. Here's another clearer example: -