I've had the same problem as (the one I had) 3 years ago.
The problem I am facing now is the same as 3 years ago.
It depends what you mean. The first sentence means what it says. The second means the problem s/he first met three years ago remains unchanged' - it could be more clearly expressed as '... the same as it was three years ago. (For me, 'the one I had' and 'it was' are necessary for clarity; but they are often omitted.)