This paper reports the experimental results related to Lineage Event storage via smart-contracts deployed on private and public Blockchains. In our experiments we measure three key metrics: the cost to deploy the storage Smart Contract on the Blockchain. This metric captures the initial expenditure, typically in gas units, required to deploy the Smart Contract that facilitates Lineage Event storage, then the time and gas costs needed to store a Lineage Event. We investigated both single and multi-clients scenarios. We considered the following public Blockchains (largely used by industry): Hedera, Fantom, Harmony Shard0, Polygon Amoy, Ethereum Sepolia, Optimism Sepolia, Klaytn Baobab and Arbitrum Sepolia. Furthermore, we investigate the performances of Hyperledger Besu with different consensus algorithms as private Blockchains. Additionally, we explore an alternative case study involving hash-based batch Lineage Event storage using the QBFT consensus algorithm on a private Blockchain, and analyze the impact of client scaling on transaction times.