In your case, I cannot tell much difference.
The following are some use cases.
If you want to refer "particular people", use 我朋友. If you want to to refer "some people", 朋友 and 我朋友 are both OK.
Not much difference in this context:
Similar in English:
- I am going to hang out with friends.
- I am going to hang out with my friends.
But we use 我朋友 when introducing people.
- 这是我朋友John. √
- 这是朋友John. x
- John是朋友。 x
I guess it is also quite the similar in English:
- This is friend John.√
- This is my friend John. x
If you want to emphasize its meaning, 我朋友 is usually better.
To express your anger or worry,
is better than
However, if you want to comfort the guy who broke the vase, you probably want to de-emphasize the meaning of it:
Alice: 我打碎的花瓶是谁的啊？ Bob:是朋友的，不用担心
is slightly softer than
Alice: 我打碎的花瓶是谁的啊？ Bob:是我朋友的，不用担心