Both compatibilists & libertarians ground choice and action in the agent's own psychology. They affirm that an agent's act of willing is rooted in who they are and involves their own experiences, habits, character, personality, goals, reasoning and weighing of motives. The act is influenced by the environment and circumstances in which it takes place
Both affirm that as the agent actively settles to a choice they move willingly to a voluntary act
The major difference is that under compatibilism the agent cannot diversify its acts during the act of willing. The choice the agent settles on is fixed by the culmination of internal and external antecedents. The agent is the product of the antecedents and circumstances. These factors are part of a causal chain that runs through the agent’s own will. Despite being part of a deterministic causal chain the will actively endorses the choice making it the agent's own
Under libertarianism an agent can diversify its acts during the act of willing. This allows a genuine openness to all available options since the agent is more than the sum of antecedents. The internal and external factors are all involved but the agent has a power to guide and control the process such that the outcome is not fixed until the agent settles. The agent is not relying on luck or randomness but is actively involved as he self-determines which option they will act upon, based on their reasoning
Both argue that the settling and resulting choice within their framework is properly attributable to the agent as the source in the sense required for moral responsibility and genuine self-governance.
Let the reader judge whether that's the case.