That may of helped here. I was just holding the camera on the railing and the fireworks are a little squirrelly
The above shot shows focus on a foreground item (the Liberty Bell) and the fireworks weren't too badly out of focus.
I think a bigger sensor and RAW helps with longer exposures. I tried some manual 4 second shots and they were overexposed, so I stuck with 2 second exposures on my point and shoot.
I do agree that fireworks are fine for any camera with a tripod.
That's a fantastic shot. Especially without a tripod. Very well done.
RAW is generally helpful for any difficult exposure, but simply because it allows for the most post processing correction. If shot correctly, fireworks don't need a ton of post processing in *most* cases. My shot above, was shot straight to jpeg, though I still changed the contrast and saturation a bit in post.
Fundamentally, I can't think of a reason why a larger sensor would be helpful for a long exposure, except for the better ability to handle noise. But if you keep your ISO low enough, shouldn't be an issue.
I'm surprised your 4-second shots were over-exposed. Was your ISO set low, or did the camera automatically boost your ISO thinking it was "dark?"
The only time I've had serious over-exposure of fireworks, whether on dSLR or point & shoot, is during massive bursts, as in a finale. Where there are lots of fireworks going off simultaneously, I see the need to keep it to 2-4 seconds.
As to focus, on a dSLR or large sensor camera, I would definitely consider setting the focus manually.
But a small sensor camera essentially reaches infinity very fast. If your shot, the Bell and the fireworks both look completely sharp to me. I don't know if the Bell would be in any less sharp, had you focused on the fireworks directly.
You have the Sony HX20? I plugged the number into a Depth of Field calculator out of curiosity. At wide angle (about 5mm?), and with an aperture of 8, the hyperfocal distance is only 2 feet. In other words, when set to infinity, everything from 2 feet to infinity will be sharp. So as long as your subject is more than 2 feet away, the focus really shouldn't be an issue.
(For times when you don't want background blur, a small sensor camera actually does have its advantages).