If BCH had the same market cap as BTC, would it be greener?

During 2017, when there huge demand for BTC, fees went up considerably. The bigger BTC gets, the more people who use it, the more congested it will get, and the higher the fees will get. One of the issues is the environmental impact this will cause because of the high energy use.

However, if BCH had the same level of demand as BTC, would it use the same amount of energy even if its block size is increased to accommodate higher demand?

Also because BTC has lightning network, which arguably uses very little energy, would this overall make BTC greener than BCH? If BCH had retained the bitcoin name and branding (rather than bitcoin cash), it likely would have become the dominant type of bitcoin, but would scaling on bigger blocks be greener than scaling via lightning network?