First, all Omega-3 products are not alike. Here's what I learned about Omega-3 from my research. The "3" relates to three sources of Omega-3 fatty acids. Two of them, DHA and EPA are found in marine products such as fish and krill. The third source, ALA, is from plants. So with fish oil you are getting two of the three sources at once. That makes sense to me as a good reason to take Omega-3 fish oil. You will also note below that many of the reasons we choose to take Omega-3 do not occur with plant-based products.
The #1 Pharmacist Recommended Omega-3/Fish Oil brand,* Nature Made fish oil supply comes from deep ocean waters, not farm-raised fish. State-of-the-art purification processes remove mercury and ensure high levels of fish oil purity and concentration, guaranteed to pass the stringent standards of the Global Organization for EPA and DHA Omega-3 Voluntary Monograph.‡
• Fish oil – Fish oil is among the primary ways that people enhance their intake of omega-3 fats. High-quality fish oils can certainly provide many health benefits. However, this oil is weak in antioxidants. This means that as you increase your omega-3 intake through fish oil consumption, you actually increase your need for added antioxidant protection.
The Japanese notably have the lowest levels of coronary heart disease mortality and atherosclerosis among developed nations — a phenomena that has been largely subscribed to diet. However, even within Japan, a 10-year study of over 41,000 people found that higher intakes of omega-3s were associated with lower risks of nonfatal coronary events (8). A more recent study also found that Japanese with higher omega-3 index levels (10%) had a lower risk of fatal coronary heart disease than those with a lower omega-3 index levels (8%) (9). The study begs the question of whether maybe even the Japanese have room to improve their omega-3 intake and whether 8% should be considered the lower limit of a desirable range.

Fish or seafood allergy: Some people who are allergic to seafood such as fish might also be allergic to fish oil supplements. There is no reliable information showing how likely people with seafood allergy are to have an allergic reaction to fish oil. Until more is known, advise patients allergic to seafood to avoid or use fish oil supplements cautiously.
Mercury and polychlorinated biphenyls (PCBs) are common toxins in seafood. Although the U.S. banned the use of PCBs and DDT in 1976, these and other chemicals are still used in half the world's commercial chemical processes. Substances like these can hang around in the air, soil, and water for many years. They end up in the bodies of fish and animals.
Fish oil supplements are available as liquids or capsules. Some capsules are enteric-coated to pass through the stomach before dissolving in the small intestine, thus helping prevent indigestion and "fish burps". Poorly manufactured enteric-coated products have the potential to release ingredients too early., a for-profit supplement testing company, reported that 1 of the 24 enteric-coated fish oil supplements it evaluated released ingredients prematurely.[48]
^ Jump up to: a b Casula M, Soranna D, Catapano AL, Corrao G (August 2013). "Long-term effect of high dose omega-3 fatty acid supplementation for secondary prevention of cardiovascular outcomes: A meta-analysis of randomized, placebo controlled trials [corrected]". Atherosclerosis. Supplements. 14 (2): 243–51. doi:10.1016/S1567-5688(13)70005-9. PMID 23958480.

Preventing re-blockage of blood vessels after angioplasty, a procedure to open a closed blood vessel. Research suggests that fish oil decreases the rate of blood vessel re-blockage by up to 45% when given for at least 3 weeks before an angioplasty and continued for one month thereafter. But, when given for 2 weeks or less before angioplasty, it doesn't seem to have any effect.