我很乐意 = I'd love to do.../ With pleasure (to help sb. or something) 我很高兴 = I’m very happy (that ...)

Note：According to my experience, people rarely use [我很乐意], especially replys to [谢谢], we just say [不客气] for short ,if you want to say it more politely, then [很高兴帮到你] seems a very gentlemen way to say [my pleasure] in Chinese to a lady.

我很乐意means i am glad to 我很高兴means i am happy but when they both express someone answers others requests, they have no big difference