It's the same. 恭喜 means congratulation! In Chinese sentences, just say 恭喜 to someone is right, but when you just say 祝賀 is weird. In complete sentence,adding the subject I(我）and object You（你），like 我祝賀你。我恭喜你 is right,too. birthday or promotion ，anything great happened to anyone,you can use those word to congratulate them.祝賀 usually using in formal.

most time they're the same meaning. but seriously "恭喜" is used in the situation that when you want to say something good or give somebody wishes and "祝賀" is a used when you're going to congratulation someone. here are some examples: 1. when the Chinese Spring Festival is coming we said "恭喜发财" to everybody but we don't use "祝贺" at all. 2. when somebody works hard and won the Best Employer Prize of this year, both "恭喜你" and “祝贺你” are possible. I hope this can help you for your confusion.

almost the same.dont get bogged in this. but if you are giving your blessings in festivals such as Spring Festival,remember to use'恭喜发财'istead of '祝贺发财'