What is cheaper Cost of Equity or Cost of Debt ?

Cheaper in what way? It depends on what your goal is?

1.) Is it to gain Capitol?

2.) To figure out default premium? Which in most cases to my knowledge debt expenses are deductible.

3.) To figure out cost of equity as a whole?

4.) To raise or lower the expected return?

Your question for me is to vague and needs more information to figure out what exactly you want to know and what the final objective to the question is. I think only then that answer can be correctly given. However, I wouldn't use the word cheaper, as a accountant or otherwise, will tell you the lesser of two evils.