Both are equally useless in the grand scheme of things, thus both will be worthless eventually. You will likely be able to make some profit from the few pump and dumps that will happen before that though.
And that grand scheme would be what? Are you willing to shed some light on this? You think that exchanges will shut down because of all the profit that they are making? Altcoins are a thing and they will continue to be a thing.
Litecoin just halved this year so there isn't really much going on for litecoin for the next couple of years. Besides litecoin has best volumes out of all cryptocurrencys besides bitcoin ofcourse. Litecoin is silver to bitcoins gold.
Doge is still better than most of the shitcoins out there. I think it will survive in the long term. However the price of 1 doge would be 5-20 satoshis max.