Are there differences between 朋友 and 我朋友 in modern Chinese?
In common context, the are literally the same.

But you can say the latter one shows 5% percent more friendship. 

Since in Chinese we often omit some obvious verbs, we can get the following equation:

我朋友的 = 是我朋友的 ~ 是朋友的


Technically they are different just like: 

tell the difference between : 

Q: where do you get this chair?
A: it's from my friend  /  from friend


People may argue about their difference. 
But As a Chinese, I would like to consider 我朋友的 and 是朋友的 the same thing under common context.