Prokaryotes are smaller than Eukaryotes (typically). Why is being smaller an advantage? Being smaller is an advantage to cells for a few reasons. One reason is that being a small, single-celled organism allows the prokaryote to reproduce quickly. By being able to reproduce quickly, the prokaryote has the advantage of mutation on its side.

DNA replication is not exact. The more often it is replicated, the greater the chance of a mutation. Lucky for Prokaryotes, mutations aren’t always negative. It is the ability to adjust that has allowed prokaryotes to survive in extreme environments. This ability also gives the prokaryote dibs in extreme living environments. since they are able to better adapt, if these environments were to become "less" extreme, the prokaryote will still be the first organism to habitate the area, taking initial advantage of nutrients. (see end of page for reproductive abilities of prokaryotes).
Gessner, Robert V. Lecture Outline and Supplement. Micro 200 Introductory Microbology.
Department of Biological Sciences, Western Illinois University, Spring 2000.

A second reason that being small is an advantage is due to surface/volume ratio. Think of it this way: the cube example below comes from here

Direct quote from above webpage
Exercise - Surface:Volume
Compare the surface to volume ratio (surface:volume) of a cube that is 1 cm X 1 cm X 1 cm with that of a cube that is 10 cm X 10 cm X 10 cm.
Smaller cube (1 cm X 1 cm X 1 cm)
The surface area of one side = 1 cm X 1 cm = 1 square cm (or 1 cm2).
There are 6 sides, so the total surface area = 6 X cm2 = 6 cm2.
Volume = 1 cm X 1 cm X 1 cm = 1 cubic cm (or 1 cm3)
Surface:Volume = 6 cm2/1 cm3 = 6 cm2/cm3 (or 6 square cm of surface area for each cubic cm of volume)
Larger cube (10 cm X 10 cm X 10 cm)
The surface area of one side = 10 cm X 10 cm = 100 square cm (or 100 cm2).
There are 6 sides, so the total surface area = 600 X cm2 = 600 cm2.
Volume = 10 cm X 10 cm X 10 cm = 1000 cubic cm (or 1000 cm3)
Surface:Volume = 600 cm2/1000 cm3 = 0.6 cm2/cm3 (or 0.6 square cm of surface area for each cubic cm of volume).

Comparison
Notice that the larger cube has more surface area and more volume but less surface area for each cubic centimeter of volume. For any given geometric object (cubes, spheres, etc.), smaller objects have a greater surface to volume ratio (surface:volume) than larger objects of the same shape.

end of direct quote from above webpage
also so here for surface volume ratio.

The fact that smaller cells have a greater surface to volume ratio is relevant because all of the nutrients a cell needs come in through the membrane. The same for the cells waste. If a cell is too large, “there won't be enough membrane to transport the amount of food in and wastes out to support that large cell size”. see here MOre on surface volume: here (from gessner source) also see:

other advantages are the prokaryotics methods of reproduction. the following links go to pages from my bio books. These are the books i used (here). if you need page numbers, call me or email me and i'll get them to you. my books didn't fit on the scanner too well. the following links should be print size. happy clicking.
Transformation
Mutation in DNA Replication
Bacterial Mating
Gene Transfer