Ani Danielian on learning Eastern Armenian after knowing Western Armenian:

if you are fluent in western armenian it will require only a very small amount of study to understand eastern armenian. mastering it is another story. the conjugations and verb constructions are quite different, and so is a lot of vocab which is easily learned. so the real difficulty is the verbs which really need to be relearned as there are structures in eastern which sound exactly like western but mean a totally different thing. like the way to say "i'm going to go" in western is the same as saying "i must go" in eastern. so that screws people up. and, of course, there are sounds in eastern which do not exist in most dialects of western, although they do exist in some western dialects. they may be difficult to learn, and also many letters in western and eastern have switched pronounciations, which makes reading difficult at first. also, many western speakers use a lot of turkish words which they may not even know are turkish, and obviously eastern armenians don't speak any turkish. and, last but not least, the accents are completely different. this wouldn't matter so much to fluent western speakers, but to non-fluents it makes things impossible. it's like a foreigner who learned british english trying to understand someone from the american south. the words are the same but they sound *so* different.
hope this helps--it's accurate as far as i know which is not very far. just don't believe those people who say eastern and western aren't different at all. they are most likely referring to fluent speakers and not people who just speak household armenian or whatever.