I would say that a good friend is someone who is able to intuit what their friend needs from them in that moment, and does what they are able to provide it.
There are appropriate and inappropriate times for both options you listed, and I think both can happily exist in the same friendship. Sympathy and solutions aren't diametrically opposed to one another.
When someone is down and struggling, throwing solutions at them can feel like kicking them when they're already down. That's when you need to bolster them emotionally, encouraging them. When they are feeling stronger or more aware of the problem from a more removed perspective, likely not in a moment of pain, they will be more open to gentle suggestions and solutions - but even then, remember that it's a discussion and ultimately not your decision.