Both have same meaning as "to report". But the usage is a little different. If you want to report some illegal things or crimes, then you can use 고발하다. And if you want to report some suspicious or doubtful things, then you can use 신고하다. Therefore 고발하다 has more negative meaning than 신고하다. I hope my explantion will be helpful to you :)

To me, 고발 하다 sounds like I have something against someone especially something illegal, then accuse the of it. 신고하다 is like no matter if they harmed you or not, you just think that they're doing something wrong and you report them to the police or something. But I'm not 100% sure cause I didn't major in Korean or something. I'm just a native speaker.

네!알겠습니다! ^^

고발하다보다는 신고하다가 쓰임새가 더 넓은 거 같아요. 경찰에/112에/119에 신고하다. 경찰서에 가서 고발하다. 언론에 고발하다.