Janice, congratulations on your new bag.
I have both the Large and the Oversized, in various colors, so I can speak from experience of having carried both sizes.
I tend to get more use out of my Large Muses than I do out of my Oversized Muses. I love the Oversized, but like you said, it can get kind of heavy. The other problem that I have with the bag is that it bangs against my leg with much more frequency than the large does. I do A LOT of walking (I live in NYC) and I find that it is much easier for me to pick my large Muse up and go. The Oversized can become cumbersome on occasion. I tend to wear it in the crook of my arm or held in my hand (don't care much for the aesthetic look of the bag when it is worn over the shoulder as I find it has a tendency to get smooshed, thus taking away from the beauty and the gorgeous lines of the bag). When the Oversized is worn in the crook of the arm, since it is so long, and since the majority of the weight is at the bottom of the bag when filled, it rebounds against my thigh sometimes.
That being said, I love my Oversized Muses and still get good use out of them. I just tend to carry my Large Muses more often than the Oversized. If I have to carry my laptop or files, or if I feel like carrying a "statement" bag, I grab the Oversized. Otherwise, it's usually the Large for me.
The Large by the way is plenty large. It is capable of holding a lot of stuff, and I think may be more practical for anyone who is on the run a lot.
Good luck with your decision.