Prokaryotic cells can be found in Bacteria and Archaea while Eukaryotic cells can be found in Protists, fungi, animals and plants. These two cell types differ in size-- Prokaryotic cells are usually much smaller than Eukaryotic ones. Also, both are surrounded by cell membranes and contain cytosol. However, Eukaryotic cells are more complex due to the presence of membrane-- bound organelles that are not present in Prokaryotic cells.
Both Prokaryotic and Eukaryotic cells contain ribosomes for the synthesis of proteins. Ribosomes themselves are made of protein subunits along with ribosomal RNA. These are found in the cytosol in both Prokaryotes and Eukaryotes and also found attached to rough E.R. and the nuclear envelope (in Eukaryotic cells only).
Homeostasis is the maintenance of a stable internal environment within a cell and allows a cell to respond to changes in its surroundings to make adjustments accordingly. This process occurs in all cell types--Prokaryotic and Eukaryotic and is vital for staying alive.
Chloroplasts are found in algae and plants which are both organisms with Eukaryotic cells. Within these organelles, the chemical reaction of photosynthesis occurs. Chloroplasts have two membranes separating the inner space from the surrounding cytosol. The pigment chlorophyll is inside along with vital enzymes which allow a producer to absorb light energy for photosynthesis to produce sugar and oxygen.
There are photosynthetic bacteria which are Prokaryotic and while they technically do not have chloroplasts, they do have vesicles with pigments that can be used for photosynthesis. Therefore, photosynthesis can be seen in Prokaryotic cells that are producers, along with Eukaryotic cells like algae and plants that can also produce their own chemical energy from light energy.
Metabolism refers to all of the chemical reactions that occur in living cells. Metabolic processes occur in both Prokaryotic and Eukaryotic cells. All cells must metabolize food to provide energy to do cellular work.
In Eukaryotes, the process of aerobic respiration occurs in organelles called mitochondria. Respiration is a catabolic reaction which results in the formation of ATP by metabolizing a fuel like glucose in the presence of oxygen. The reaction produces ATP which is used as a form of energy currency cells can use for life processes and it produces the waste products carbon dioxide and water.
In Prokaryotes, some cells can perform aerobic respiration, some perform anaerobic respiration or fermentation to obtain energy from food without the presence of oxygen. An example of a prokaryote that ferments is lactic acid bacteria which derive a small amount of ATP from glucose by converting it to lactic acid. Anaerobic respiration occurs in the cytosol of prokaryotes or on the inside surface of the cell membrane. These organisms lack mitochondria and other membrane-- bound organelles.
Any living thing needs a source of energy to stay alive. Organisms whether Prokaryotic or Eukaryotic are open systems which rely on a steady influx of energy into the cells so that work can continue and life can go on.
I have included an excellent link which compares Prokaryotic and Eukaryotic cells.