I think it'll go something like this
Mass dumps of BTC because everyone wants to earn as high a ROI as possible and ASIC miners are useless for anything other than SHA256 hashing. Falling BTC price will facilitate more mass dumping.
People GPU mining all move to LTC because BTC hash rate is too high.
LTC hash rate skyrockets, LTC goes up in value massively.
Right now I hold 50% BTC and 50% LTC. It's clear that the value of LTC is stable, as people (like me) are constantly dumping BTC mined into buying more LTC.
I think it will follow the same path as Namecoin after merged mining
Hash rate skyrockets -> people with coin of little use -> dump it like ugly prom date
All merged mine coins will fall into this trap because people acquire them for no extra cost and so just dump them. LTC will never be able to be merge mined with BTC, so it doesn't have that problem.