Let's get Polygon out, because they are not a base-layer blockchain.
> a similar number of transactions to ethereum (or more), with lower fees.
Are we talking about the base currency (Wei) or the dollar-equivalent amount? If Wei, the only way that the transaction fees can be lower is if the chain has a different set of costs for the operations.
If you are talking about the dollar-equivalent amount, then yes, transactions are going to be "more expensive". But even then, it is not related to the consensus algorithm and just the "price of the base token".
Transaction volume meaning.. the number of transactions processed by the network?
If you meant monetary volume, you should have used a different term than one which is well-recognized to refer to the number of transactions (both in and out of blockchain applications of that term)
edit: I see, you're suggesting the fees are cheaper because the token is cheaper, and somehow seem to think EVM networks will have a straightforward relationship between the number of transactions and the cost denominated in their gas token.
I don't see how this follows. The fees are entirely a function of network constants and usage, which have more to do with what people are willing to pay to get their transaction into a block.
Ethereum has a limited amount of block-space, and a fixed number of blocks per year. The gas price isn't entirely a bidding system, because there's basically a floating multiplier which adjusts automatically based on the "fullness" of the most recent however many blocks, but the principle is that you need some form of congestion control
In blockchains which have larger blocks, or more numerous blocks, or a number of blocks/block-size which adjust based on usage, it is not as costly to get a transaction included.
So I don't know about Cardano or Algorand, but many networks can handle as many transactions as ethereum while having much cheaper transaction fees, which seemed to be the point you were arguing against
> a similar number of transactions to ethereum (or more), with lower fees.
Are we talking about the base currency (Wei) or the dollar-equivalent amount? If Wei, the only way that the transaction fees can be lower is if the chain has a different set of costs for the operations.
If you are talking about the dollar-equivalent amount, then yes, transactions are going to be "more expensive". But even then, it is not related to the consensus algorithm and just the "price of the base token".