I mainly take pictures of my grandkids playing, some scenery and birds. I am looking for an autofocus type camera that has a good zoom, one that will shoot quickly in low light situations. I miss a lot of photos while my current camera, Canon SD1400 IS, is trying to focus.
What particular specifications should I be looking for in an autofocus type camera for daily use?
If you are serious about fast autofocus and low-light performance, you will have to consider cameras which can satisfy those needs. You cannot decide between models when neither distinguishes itself for your needs.
Low light performance requires a larger sensor. Incidentally, more sensitive cameras often autofocus faster too. The other major factor is the lens, a bright lens lets more light in which is better for low-light performance and - again - autofocus.
Both cameras you choose have long and rather dim lenses too which does not help you. It difficult to manufacture lenses with a long reach while keeping a bright aperture, so you will have to compromise somewhere. Since you like to shoot birds, I would favor a long lens and get a Nikon DL24-500. It also employs Phase-Detect AF which should speeds autofocus up considerably.
Should you decide that low light performance is more important to you than reach, there are several cameras with large sensors and bright lenses. Consider the Canon Powershot G5X, Panasonic Lumix LX100, Canon Powershot G7X Mark II or Sony Cybershot RX100 (III or IV). These have a much short reach, around 4 or 5X zoom.
If you want something that does low light and fast autofocus, chances are good you'll need to double or triple your budget and get a substantially different type of camera.
The bridge cameras you're looking at are built to be low-cost versatile superzooms, where most of the money has gone to getting you super long reach. But it gets there with a combination with a very small sensor and a relatively slow lens.
Low light capability typically requires a larger sensor and a fast lens, both of which add substantially to the size/bulk and pricetag of a camera, reduce the reach of the lens, and also can create issues with accurate focusing.
Bridge cameras also typically autofocus by contrast detection off data from the main sensor. Fast autofocus typically requires phase detection of some kind--either with dedicated photosites on the main sensor, or a separate AF sensor array. And again, this adds substantially to the cost, and makes handling more complex.
Most folks go the dSLR route, but this can get very expensive and heavy and bulky and for some people can be overkill. It's also very expensive to get a great lens for birding in this type of setup (ok ones are around $350, though).
If you are unwilling to give up reach or small size and you're willing to double your budget, you could look into the Nikon 1 system. The 1"-format sensor is a good compromise between the larger more expensive APS-C and full-frame sensors of dSLRs and the tiny 1/2.3" format sensors in bridge cameras, and would still give you some reach with a relatively inexpensive lens. And unlike most mirrorless systems, Nikon 1 is known for fast accurate AF, as it has phase detection photosites on the main sensor, and the small selection of lenses may not be an issue for you. Also, the system is old enough now that first-generation camera bodies can be found used for under $200. It will still be more expensive than getting a new bridge camera (lenses), and the low light performance won't be as good as a dSLR, but the added function may be enough.
