Which is the most profitable in the future, Bitcoin mining or Ethereum mining?

There are plans to make ethereum proof-of-stake in the future. (Casper) As far as I know bitcoin's future plans still involve SHA256 hashing

In my opinion ethereum staking in about 10 years give or take will be more profitable than bitcoin mining.

Bitcoin could be more valuable in the future if there is high demand and scarcity of supply but that doesn't necessarily mean that mining bitcoin will be profitable. The supply is capped and bitcoin halving over time will make less and less bitcoins harder and harder to generate.

If the majority of the population of the world moves to cryptocurrency I imagine a rare crypto like bitcoin might be hoarded like rare books or pieces of art and each bitcoin might be kept for years by each owner and occasionally auctioned off to a new owner. More plentiful cryptocurrencies such as ethereum could continuously keep being generated with more abundance and ease compared to bitcoin. Also, since there are far more uses for ethereum such as smart contracts more people would be willing to pay because of ethereum's utility.