Present perfect and Past perfect continuous.?

Both your sentences are Present Perfect, but the second one is also Continuous, or Progressive.And in both cases, it is clear that you are still living in London.

We often use them interchangeably, but most teachers would tell you that "I have been living in London for three years" carries a slight suggestion that you may be moving on somewhere else in the future."I've lived in London for three years" doesn't carry that  suggestion - but the possibility is not ruled out.

 The examples from @Sweetness are good ones.

1, I've lived in London for three years and have never seen any crime.But2, A: Hey, I haven't seen you for ages! Where have you been?

B: Oh, I've been living in London.This suggests the conversation is taking place somewhere other than London. For example, B used to live in Montreal. So when A bumps into B and asks where B has been for so long, B replies that he's been living in London, which is clearly not his normal home.

"I have been living in London for three years" suggests it's not permanent.

The second sentence is still present perfect, which you probably knew. 

In any tense, the continuous and the simple forms are sometimes interchangeable, or almost so. "My son goes to Trump University." "My son is going to Trump University."

In the example you give the two sentences are usually interchangeable, but occasionally the first, but not the second, might be used for a completed activity. "I've done a lot of things in my life. I've sailed the seven seas. I've climbed Mount Everest. I've lived in London for three years."

BTW it should be "I've been having trouble" not "a trouble" and you could equally well have said "I've had trouble understanding the difference" or even "I have trouble understanding the difference." Sometimes the present and the present perfect are interchangeable too.

The first sentence would typically be said if you had more to add to it by way of a reason for saying it. 

Example:

'I have lived in London for three years, and in all that time I have never seen any crime on my street until now.'

The second sentence is used more as a response, as if someone were to ask you where you have been, or how long you have been where you are now. 

Dave- JOE!! I haven't seen you in ages! Where have you been?

Joe- I have been living in London for 3 years.

They mean the same thing. The only difference is whether you want to emphasize the length of time. It's your decision which one to use. Please disregard the other answers. You have NOT used the past perfect, and both sentences say that you still live in London.

I have only live in London for 3 years, so I'm not considered a native.

I have been living in London for 3 years, so I know my way around really well.

It all depends on whether you want to indicate that it's a long time or not. 

Unlike the first, the second one suggests that you are still living in London; this is present perfect continuous.  The first sentence does not preclude the possibility that you may no longer be living there.  Much depends upon the context.