An HDS with the extra sonar module produces way better images than an Elite. Hands down better, and it is much more responsive. And if you are considering an HDS Carbon the screen quality and touch is more reactive. But then again, there is a huge price difference. If you don't mind paying more, or want a unit that will be comparable to the best for a number of years, get the HDS. If you can, go look at them instore. Demo images are almost always a tad better than what most people get, but even on the demo images the difference is clear.
An Elite isn't a bad unit. My buddy I go fish with every other week has one and I like using it. I personally went with a Garmin since it was cheaper and I liked the traditional sonar, but would be happy with an elite.
You can't go wrong on your decision here, but you can spend a ton of money.
I'll also throw a recommendation on the new Humminbird Solix 10. It has the best down and side imaging available. But I've never found the traditional sonar to be that great.