Your question is a good one. And it would be great if more people took some time to study the answers. (And I’m not even an Identifier!)
First, I don’t really agree that it all comes down to camera quality, or power. Today’s small sensor cameras are very capable and let’s not forget that they have more resolution than the digital pro DSLRs of only, what 15 years ago?
But another area you might want to consider is post processing. I buy my camera now based on my software and skills as much as I do anything else. Why? Sure. Cost is a BIG factor for this pensioner. But also, so is the camera size/weight and ‘PF’ – preciousness factor.
Small sensors are generally much lighter than DSLRs and even when they’re not, they can pack a tremendous amount more zoom into their closed lens system. And that’s the preciousness factor too: with no option to change the lens, using a small sensor bridge camera means you never need to worry about changing lenses and exposing camera guts to the winds of chance with an in-field lens change. (Winds that often include sand, pollen, and other airborne particles)
Lighter/one-lens bridge cameras are just more opportunistic when it comes to grab and go, as well as easier to keep an eye on and less tempting to any would-be thiefs. And, if you ever encounter accidental disaster (‘Oops, where did that cliff come from?’), replacement is not going to kill your photo career based on finances.
Back to software.
I took your original image JPG, and ran it through some standard steps I use in a lot of my photo rehab and here’s the results:
The nice thing about software is it’s not that ‘tied’ to your camera model. Old, new, bridge, DSLR, jpg, RAW – a lot of it just works. And many good editors, some even free, some work on your phone.
I think I would have appended your question with:
“… without motion blur.” because so many of the other answers here attacked that side of it. Yes, the shutter speed is critical and all other factors have to take the back seat to it – but so is focus tracking, whether it exists or not in your camera. ESPECIALLY true for BIF (Birds in Flight) shots.
The simple answer to shutter is ‘as high as you can get away with’. And to that end, this is where RAW as an option truly comes into play. Why? Because RAW post-processing allows you to shoot in that apparently ‘horribly noisy’ high-ISO range and remove most of the noise and recover detail!
Plus, RAW editing can even often retrieve blown out highlight areas and deep shadow detail that you thought was just lost completely – judging by the camera preview.
I use MOSTLY a small sensor, superzoom (Nikon P950) for birds and/or insect macro (another big advantage if you carry a little Raynox macro clip-on in your back pocket). Here’s some samples (all handheld) from that cam that are pretty typical for me these days:
BIF, actually a single frame from a short 4k video clip with manual shutter speed set to 1/2000s (within the 1/30s frame). This is another ‘hack’ that works for me, also with quick bugs: you get 30 frames per second of shooting and you’re more likely to get ‘something’ decent.
BugIF
But you don’t need to go for an ultrazoom bridge to get good results. I took this one last week while pulling a wagon with two two-year-olds, from across the street, and using my old Powershot 540 (bought it used two years ago, for $150):
No, not a BIF, but it shows that low pixel sensors do not mean the same as low quality. Gotta run. Back later if you have any questions.