Plants and algae in an aquarium don't compete for nutrients. Algae require very, very little nutrients, so there is always plenty in the tank for them. Plants require many times more nutrients, so whatever the algae consume doesn't affect the plants. But, for some reason, healthy fast growing plants tend to keep algae from even starting a colony in an aquarium So, the objective is to have lots of healthy plants, preferably fast growing ones, in the tank, so algae won't even start to grow.
The more light you have, the faster the plants try to grow. If they are short of some or all nutrients they won't be healthy plants, and unhealthy plants attract algae. The faster they grow the more difficult it is to keep them supplied with all of the nutrients they need, but it is extremely difficult to keep enough carbon available to the plants (CO2). "Low tech" tanks don't have a CO2 system, so it is obvious that a successful "low tech" tank has to have low light. But, too low light will also prevent the plants from growing at all. So, a "low tech" tank has to have the right amount of light, more than anything else. See http://www.plantedtank.net/forums/showthread.php?t=184368 for more information.
The more light you have, the faster the plants try to grow. If they are short of some or all nutrients they won't be healthy plants, and unhealthy plants attract algae. The faster they grow the more difficult it is to keep them supplied with all of the nutrients they need, but it is extremely difficult to keep enough carbon available to the plants (CO2). "Low tech" tanks don't have a CO2 system, so it is obvious that a successful "low tech" tank has to have low light. But, too low light will also prevent the plants from growing at all. So, a "low tech" tank has to have the right amount of light, more than anything else. See http://www.plantedtank.net/forums/showthread.php?t=184368 for more information.