Unless you are tuning down by at least one step, you should NEVER use heavy gauge strings on an acoustic guitar. The top and the neck are not able to handle that kind of tension. Remember, all guitar builders and designers are walking a fine line between a guitar which can handle the tension involved and sounding good. We try to build them as lightly as we can to make them sound good, without blowing up. Any factory guitar should be able to handle mediums without problem, but heavies are just to much.
As to your question, yes, there is a huge difference between lights and mediums. I usually like the sound of mediums more, but I have pretty severe hand problems so I use lights on most of my guitars. We string up almost all of our guitars at the shop with medium gauge strings when we ship them out, unless we have been asked to do otherwise. The exception to this is our small bodied Parlor guitars, which seem to be overdriven by the mediums.
Bob Taylor has fairly strong opinions about this. It is his opinion that anything smaller than a Dreadnaught or a Jumbo should be strung up with lights, because he thinks the tops sound better when they are not forced to move so far. I have a different view, though, as I find the lights do not give as wide of a dynamic range, which is very important to me. I want a guitar which sounds as good when you are lightly fingerpicking as when you are strumming like a weight lifter on amphetamines. I find this is difficult with light strings, but mediums do a great job of it.
Just a little story about heavies. I have a little copy of an old ladder braced Gibson L-0 which I made about eight years ago. It has a short scale, and I was needing to tune it down to a C# (I was trying to learn some Leo Kottke song, and he tunes down that far) so I strung the guitar up with heavies so that it could handle being down that far. Not thinking too much, I took the guitar to a class, which meant I had to tune it up to standard pitch so I could play with the rest of the class. I like the sound so much that I mistakenly left it that way. About a week and a half later, I noticed the shape of the braces transferring through the top. Too much tension and it did not take long to do it. I now keep that guitar strung up with mediums, because it just doesn’t sound right with lights. It has stabilized with the mediums, but I still have to keep an eye on it because of the damage I did when I put those heavies on.
Light
"Cowards can never be moral."
M.K. Gandhi