显得 and 看起来 all mean look (like) ,seem,appear, mostly are same, but 看起来 always INVOLVE your opinion，what you see, what you think, 显得 means someone or something SHOW status/state/emotion/condition ect. 他看起来很高兴 he looks very happy(when i see his face i think he is happy) 他显得很高兴 he seems very happy（his smile show that he is happy) the subject of 显得 is living thing in general. 看起来 both living thing and objective object 天看起来要下雨（Right) 天显得要下雨（Not wrong,but strange，we dont say a sentence like that) 这看起来很好吃（Right) 这显得很好吃（（Not wrong,but a little bit strange)

we always make some prediction on objective things when used"看起来". 这件事看起来好像是他的错。 这个裙子看起来小了。 but if we use "显得",we are expressing our subjective feelings. 他显得很不高兴。 他这么做显得他很小气。

看起来and 显得 ， both of them mean " seems like , looks like " , not so much difference .In most cases , they can be switched . eg. 这件衣服看起来有点小 vs 这件衣服显得有点小 . Both of them are ok . But in some particular sentences , it may sounds strange to switch them . eg. 他今天看起来心情很不错（ ok ) 他今天显得心情很不错（ not wrong , but we do not speak this way ） 看起来 is more commonly use than 显得，so next time ,when you are not sure to use which one , you can use 看起来。