I have mixed feelings about the question of whether to change in over here, before your trans-Atlantic flight, or whether to change when you get to Europe. On my first trip to Europe (1987), I flew to Brussels with changes in both Boston and London. The Boston change was fairly painless; the London one, not so much. We spent hours in the international lounge at Heathrow in what for us was the middle of the night. It was difficult to stay awake and not miss our connecting flight to Brussels.
So, do you want to change in the US, when you are fresh and familiar with the language, but your flight options if you miss your connecting flight to Europe are limited, or in Europe, when you are jet lagged and don't understand the language, but you have far more options for connecting flights that day. Seems like six of one, half dozen of the other.
Fortunately, since 1987, I've never had a worry about that. I have always gone to Germany (FRA or MUC) and it's mostly been on Lufthansa (my preferred airline) and a lot of flights have been on a non-stop flight (Lufthansa) from Denver. I've had other flights on NWA (now Delta) from Detroit, USAir (now American) from Philly, and United, although the United flight was booked with United to EWR, but the trans-Atlantic leg was Lufthansa.
A few years ago, I took my partner to Germany using United point (earned mostly on Lufthansa flights). Because we were using points, we had few alternatives, and although we did fly Lufthansa over we had to fly United back. She was very impressed (depressed) with the difference in quality between United (poor) and Lufthansa (good) service. Since then she insisted we only fly Lufthansa; no more United.
So, looking at your options, United via EWR to Vienna, although I would normally eschew United, only the Charlotte to Newark leg is United, a three-star airline. The Newark to Vienna leg is on Austrian Air, a four-star airline, at least a cut above United. Then the good and the bad. The good, you'll have plenty of time to make the connection in Newark; the bad, you'll have plenty of time, 8 hours, to make the connection in Newark, at least from the only connection I find on the United website.
For the Delta option, in FRA Delta uses the Terminal 2, where both D and E gates are in the same building. You'll still have to go through immigration, and maybe security after immigration, but everything is in the same building.
As for the connection through Paris, I don't know anything about it, and I don't want to know.