Simple and basic are not completely synonymous, although they are generally similar. According to the OALD, basic means:
forming the part of something that is most necessary and from which other things develop
So something is basic if it can serve as a building block for other things. For example, an atom could be considered a basic part of chemistry because other compounds build up from it.
not complicated; easy to understand or do
Some people may say that an iPod is simple to use--it is very intuitive. An iPod, however, is complex and wouldn't be described as basic.
So in your case, I would think that it depends on what these "ways" are. If the non-complex way is the building block for the complex way, use basic. If both methods accomplish the same ends, and don't overlap as much, use simple.
Note that you can consider the two words synonyms if you use secondary definitions. You could use either word, if you wanted, and still be correct.