If you break down the chemistry, "powerful" would be based on many things in detergents, but mostly phosphates. Phosphates have been removed from detergents (by law), therefore, they no longer perform in hard water as well as they did when they contained phosphates. Detergent formulas are changing all the time to include new chemicals - this link may be helpful:
You can boost your detergent performance by adding phosphate-containing Cascade Dishwasher Detergent - especially in the whites load (Cascade also has enzymes in it for cleaning those organic stains like grass stains and mustard), or add STPP (Sodium tripolyphosphate) - http://ths.gardenweb.com/faq/lists/laundry/2003052601018823.html
. STPP will stop the white "dust" from minerals in hard water from settling on your dark clothing - which is a hard water issue, not the power of the detergent. Mexican detergents, like Roma (I've seen it at Big Lots), Ariel, and FOCA still contain phosphates. So if you have really hard water, a phosphate-containing detergent may be the better choice.
Naptha (which was the cleaning solvent in bars of Fels Naptha) was an excellent cleaner, but it's since been removed from laundry products because it may be carcinogenic. You can still purchase naptha as an industrial cleaning solvent.
All detergents lose their "power" in cold water, even the detergents designed to be used in cold water. Detergent manufacturers and care labels define cold water as 80-85°F. If the temperature of water is too cold for your hands, the detergent will NOT activate and clean effectively. Cold water below 65°F is NOT recommended for washing. Even here in central Kansas, our cold water is 72° today, and it's MUCH colder for most of the year. Newer washing machines will actually add hot water even on the COLD WATER WASH cycle in order to keep the cold water from being too cold for detergents.
Hot water is also a key to clean clothes, that has been poo-pooed of late. Hot water is suggested for removing dirt from heavily soiled items - detergent alone may not be enough.
Other old-fashioned laundry aids are pre-treating and soaking. Once again, detergent alone may not be enough for heavily soiled clothing.
Depending on how hard your water is, you may need to use more detergent, as well as hot water, if body oil and dirt aren't coming out using the regular amount. So the correct amount of detergent can be a key to the "power".