Watching the fluctuations of BTC, ETH, and LTC they seem to be fairly strongly correlated with each other, at least over the last ~month or so, and increasingly so coming to the present time. It will be interesting to see if in the coming weeks and months they continue to track closely to each other or if they once again diverge.
Watching trends without an analytic platform, I have seen that over any period of time longer than ~1 day, ETH seems to perform better. It is common to see periods of an hour, up to a day, where BTC does perform better. (For this reason, not more than just a few weeks ago, I took most of my tiny collection of BTC blue chips and traded them in for ETH.)
It would be hard to believe that nobody has tried writing arbitrage bots. I would probably be overreaching to say that this effect is due to a large number of arbitrage bots (and likely also non-robots), but it seems like there are clear opportunities for arbitrage and likely that there are skilled individuals taking advantage of these chances on the regular.