Have lived vs. Have been living

The difference between your two examples isn’t great, but, depending on context, A might give a slightly stronger impression than B that the speaker will continue to live there.

The difference is more apparent in a pair such as:

I’ve been reading your book.

I’ve read your book.

The first suggests that the speaker is still reading it, whereas the second suggests that the reader has finished it.

The present continuous tense is normally used to express an action that is temporary in nature. If you were to say: I'm living in a flat, some might interpret it as not being a long-term arrangement.

Likewise, the present perfect continuous conveys continuity and can emphasize its transitory state.

I have been living here for five years.

The above suggests that the person could one day change residence, it implies it is not a permanent situation whereas the present perfect tense is more suitable for lengthier periods of time. Contrast the earlier sentence with this one:

Anne has lived here all her life.

Anne is 65 years old, she has never changed residence and is unlikely to ever move. The action is not only continuous but it also suggests permanence.

The following interpretation is taken from the book Common Mistakes in CAE. Cambridge University Press by Debra Powell.

We use the simple aspect of tenses for actions which we think are:

• finished: I've done my homework. (the homework is finished)

• permanent: I've lived in England for 10 years. I've worked for this company for most of that time. (I think I will remain in England and continue to work for the same company)

We use the continuous aspect of tenses for actions which we think are:

• unfinished or in progress: I've been doing my homework. (it isn't finished yet)

• temporary: I've been living in England for six months. I've been working as an au pair. (I think I will leave England one day- my job is temporary)