As far as I can tell, both mean foolish. Checking a dictionary, 愚かしい is defined as 愚かである。ばかげている。which does not help very much. Is there truly no real difference?
愚か（だ） describes the quality of "absent of wiseness", while 愚かしい, as with many i-adjectives that end in -しい, indicates a kind of mental perception such as sense, emotion or impression. In this sense, 愚かしい is actually telling "felt unwise" or "as if the unwise do", which is interestingly close to English approach to say foolish that is fool + -ish.
Thus you can say these two has slightly different connotation when both are usable:
(emphasizes how nonsense of (people to do) wars)
(emphasizes how (people doing) wars look irrational)
And it's not totally impossible to find some examples only either one sounds valid:
○ 愚かな人間には理解できない foolish humans will not understand
The latter is unacceptable because 愚かしい does not imply inherent, permanent character of foolishness.