EPS vs Dividend Yield

I don’t know what you mean by “the same objective” because they are looking at completely different things.

EPS is total profit available for shareholders divided by the number of shares.
On its own it means very little because it takes no account of the market value. However looking from year to year does indicate whether the business is more or less profitable for shareholders.

Dividend yield is the dividend per share as a percentage of the market value per share.
It clearly does take into account the market value. However, it only looks at the current dividend and ignores potential future dividend growth.