I feel like we may see extraordinary demand to Ethereum Classic in next bull run just because reason Ethereum went POS. But does it mean anything special? I don't think so. Ethereum is Ethereum because there are many projects over its Blockchain. Ethereum established whole new ecosystem which is nearly impossible to leave when you join. On the other Ethereum classic is just like another shitcoin in coinmarketcap or coingecko.
Previously, ETC faced a lot of difficulties because of the competition of ETH, but now that ETH has completely moved to POS, the future of ETC will be a bit more positive. But it all depends on the miners, these miners don't want to lose their jobs when ETH leaves the POW so they will look for an alternative, be it ETC or ETHW. Currently, I see that ETHW is still very new, so it is of more interest to the community, so miners will also switch to ETHW, but in the long run, I still don't know what will happen. These two coins certainly can't compete with ETH but they have a chance to go up as they represent ETH in the POW version.