But even I'm wrong here, and ltc would thrive if btc got dumped to smithereens, I wouldn't say that's a good reason to invest in ltc. That means you are placing a bet that btc will get knocked not only from the #1 spot, but get killed in a dump. Yeah, sure, it could happen ... but I wouldn't want to bet that it will happen.
I'm not in Litecoin because I believe it has the potential to take over Bitcoin's spot...I still think that's wholly unlikely. However, I'm a BIG believer in choice, and not having only one point of failure.
I always liken it to the situation we have with the internet, today. We have protocols that drive the network that have forced developers to shoehorn things into it that perhaps it's not best suited to...streaming media would be a biggie. If we had started with multiple networks, one could have evolved to specialize in streaming media and now you would possibly have a much more efficient way of getting video/audio across the network, more bandwidth (or less required bandwidth) and who knows what else it may have opened up, to have an alternative. The point is, having a choice breeds innovation.
At the protocol level, Litecoin has some significant differences that may ultimately lend it to applications that Bitcoin doesn't. It is insulated from certain issues in the Bitcoin core development, because it is a separate team (although they work closely with the Bitcoin developers) and they have a different design philosophy, in many ways. Bitcoin is going to be under tremendous political pressure from developers and elsewhere to be this or that, whereas Litecoin has less pressure to accommodate. So no...nobody's going to convince me that it isn't a big positive that we have Litecoin around.
