First off, the Nessebar View complex is not in Nessebar, nor is it in Sunny Beach, it lies between the two, so you will have a longish walk (2KM to Sunny Beach, and twice that to Nessebar) although I see the complex offers a shuttle bus.
Nessebar & Sunny Beach are chalk & cheese. Having revisited Sunny Beach this summer for the first time in 6 or 7 years, we were disappointed at the changes we saw - it just wasn't the same place we remembered. That's not to say it does not offer a good holiday, because it does, and obviously it suits many people, but it is a big resort, and is brash & in your face along the promenade area, with quieter areas further back. It does offer something for everyone, and your teens will probably enjoy it immensely.
We stayed in Nessebar, and, although there were a number of hotels & apartments going up in the New Town, both Old & New Nessebar were much more to our personal taste, being much more laid back, and quieter, especially at night.
So it really depends on what you like doing as to which you'd prefer...
Food is fine, weather in August should be hot, and in 10 years of visiting Bulgaria I have never been, or met, a victim of crime. Not to say it doesn't happen, but...
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