In general, I actually thing uneducated listeners might get a better emotional response since educated listeners are often too caught up with hearing details. I know people who say they can't just listen to music anymore because they are constantly analyzing the chord progression and all that. Luckily, I am not one of these people. I know that when following along in a score to a piece of music, I miss something in the music. A note becomes an eighth note or a 16th, not a unit of time in sound. Sometimes, I think an uneducated listener gets a better response since the magic is still there for them. They don't know what's happening, they don't know how it's happening, they just know that it is happening. I don't get that feeling too much with piano music anymore. I get it with orchestral music still though, but I don't like most orchestral music as much as piano music.
So, there I talk about one who is educated on how music happens. Knowing all that can take away some of the beauty of it for me. But being educated in that you are familiar with the style of music, that increases the beauty. To someone who doesn't listen to classical music, Mozart, Beethoven, Bach, they're all the same. Knowing the differences there and being accustomed to classical music is an important part of appreciating and enjoying the music, I think. I've listened to albums (of non classical music) numerous times before and hated it the first listen. I didn't get why anyone would like it. Then, after 10 or so listens, it became not just okay, average, or good, but excellent, one of my favorite albums ever. Good music takes time to sit in, whether it be a single piece or a genre. So yes, I think one who listens to classical music at least somewhat regularly and has acquired a taste for it and has an understanding of many of its nuances, from a listener's perspective, definitely helps you enjoy the music on an emotional level. But I don't think that's what you're talking about, is it?
The one thing studying music has really helped for me is hearing a lot in a piece that most people wouldn't hear up to tempo. Playing through a piece very slowly, hearing every chord switch, every harmony, every inner melody...that's a beautiful thing, and I think the fact that I have done that with a piano piece helps me hear all those things in a piece I've never even heard before, much less played. Things like that really do make music beautiful to me in a way I don't think it would be if I hadn't done that.
There have been times I'll be listening to a piece with others and I'll be nearly in tears, and they seem oblivious to the beauty that I'm hearing. I don't know if that's related to their state of mind, a "classical music is dumb" mentality, a lack of exposure (so it all sounds the same), or what, but I do find it disheartening. However, there are times I've listened to a piece I like, but don't get choked up over, and I'll see someone I'm with is really overcome with emotion from it. I think a lot of it is taste, too. Not everyone finds the same things beautiful. Also, I think a person's natural inclination towards intense emotion affects it. I guess I'm not even sure if that varies from person to person, but I think it does. I know a lot of people, myself included, who don't wear their heart on their sleeve, but still obviously have very high feelings, apparent when they try to put their feelings into words. Then I know people who might even be visibly very emotional but seem to have the emotions of a toddler, like "I didn't get my way and am sad/mad" or "I got my way and am happy." I guess I don't know if their emotions are actually shallower than other people's but I think there is at least some variance in that. I try not to make judgments like that though, since obviously I have no idea what these people are actually feeling.