The first sentence - 'We have been friends for 10 years ' - is correct.
There are two mistakes in the second sentence:
The first is the tense. If you are describing a situation which began in the past and is still true today - and you are saying how long this has been the case - then you must use the present perfect (have been).
The second is the use of 'since' . 'Since' has to be followed by a fixed time in the past, such as a day, a date, a month, a year. 'since 10 years' is not possible. Possible corrections of the second sentence could be:
We have been friends since 2003
We have been friends since we were children.