I've borrowed the following from the British Council as it's a very complete answer. However, before you start to read it, I should mention that the 3rd and 4th notes seem to be the most important and common differences between the two tenses. Anyway, to be loyal to the original post, I won't change the order.
Present Perfect Simple and Present Perfect Continuous
We use the present perfect tense to talk about things where there is a connection between the past and the present.
He started writing books at some time in the past. So far, he has written 16 books. He may write more books.
As well as the present perfect simple, we can use the present perfect continuous tense to talk about events with a connection to the present.
1 Look at these 2 sentences:
- I’ve been decorating the house this summer. The focus is on the action – decorating – and the action is unfinished.
- I’ve painted the living room blue. The focus is on the finished result. The activity is finished but we can see the result now.
We use the present perfect continuous when the focus is on an activity that is unfinished.
2 Look at these two sentences.
- I’ve read that book you lent me. I finished it yesterday.
- I’ve been reading that book you lent me. I’ve got another 50 pages to read.
The present perfect simple (I’ve read) gives the idea of completion while the present perfect continuous (I’ve been reading) suggests that something is unfinished.
3 Look at these two sentences.
- She’s been writing emails for 3 hours.
- She’s written 10 messages.
The present perfect continuous (has been writing) talks about how long something has been happening. The present perfect simple (has written) talks about how much/how many have been completed.
Oxford Practice Grammar highlights this issue, too.
4 Look at these two sentences.
- I’ve worked here for thirty years.
- I usually work in London but I’ve been working in Birmingham for the last 3 weeks.
We can use the present perfect simple to talk about how long when we view something as permanent. But the present perfect continuous is often used to show that something is temporary.
Please note that we normally don't use the PPS with a state verb like know, have, be, etc.
In summary, I think the main (not the only) difference is that we use the Present Perfect Simple to mention the result of something and the Present Perfect Continues when we think of the activity itself.
For more information I refer you to the "Oxford Practice Grammar" unit 17.