Why do methylamine and ethylamine have nearly the same basicity constant?
Ethylamine has a pKb slightly greater than that of methylamine.

As you are saying


  It is known that ethyl is better than methyl for inductive effect. It's positive inductive effect is greater than methyl.


is absolutely true. But the basicity in aqueous medium is not only determined by +I effect but also solvation of substituted ammonium cation.

Even though +I effect in ethylamine is more than that in methylamine, ethylamine  is more bulkier and sterically hinders the formation of intermolecular H−bonds with water.