In the long run Monero will do well assuming the level of current development continues.
We all know DASH is trash (and their new model of increased mining rewards going to masternode owners discourages adoption by new small users) buts its decline does not have a direct impact on Monero.
I have never been good at predicting what will happen with LTC so I have no comment on that.
Yeah! Hard to predict what will happen to LTC; but XMR will be a good candidate as a substitute for Dash, that's for sure.
At least it has a reasonable amount of volume to do some good trades.
The advantage that Monero currently has over virtually every POW coin and this includes Bitcoin, is that Monero has a current working solution to the scaling of blocksize question. One needs two things 1) Adaptive limits 2) A tail emission. Solving this problem without a tail emission is far from obvious, In fact I am not even convinced one can even create a viable fee market in the absence of an emission. There is a reason why there is so little progress with the blocksize debate in Bitcoin.