Bitcoin has been established since 2009 - it has the network effect, is recognised as digital gold and is the grandfather of all crytpocurrencies. It is recognised as the branded cryptocurrency and is used to transfer monies internationally (sometimes illegally, sometimes not) quickly and effectively.
Dogecoin has a picture of a dog on it - it is a currency that was initially started as a bit of fun but has no real fundamentals to it.
I know which coin I would hold (and indeed do hold), but the decision is yours. Please do your own research.