The use of 'coward" as an adjective is documented but old. It is not important in modern English.
Both of your sentences are correct and convey the same meaning.
Student or Learner
Most dictionaries classify "coward" as a noun and "cowardly" as an adjective. However, in two dictionaries (Oxford dictionary and Merriam-Webster) I have found that "coward" can also be an adjective.
All the sentences I have come across use "coward" as a noun. So, is there a situation where I should use coward as an adjective or can I stick to what I have read and always use "coward" as a noun and "cowardly" as an adjective?
P.S. Is it possible to say both "He is too much of a coward" and "He is too cowardly" to convey the same meaning?
Oxford do say it's literary.