I guess I'd like more definition on your requirement(s).
So far, we have:
excellent quality video
good low light behavior (important, not a "deal breaker")
capture stills and video simultaneously
"hate" video distortion, noise and unclear things
home and gym-based sporting events
record standard definition out to DVD recorder - want a "better way" to record to DVD
At this point, I insert the comment that sometime I come off sounding like a jerk. That is not my intention. I truly want to help - and in that process will clarify or ask for clarification...
Any camcorder can provide "excellent quality video" when the camcorder is used within its limitations. Stray from this simple statement and expect less than "excellent quality video". Two of the biggest reasons some camcorders are more expensive than others are: (1), large diameter lens. Big, good, glass is expensive to make. This large glass feeds light onto the imaging chip. Bigger imaging chips (silicon) is also expensive to make. While you don't necessarily *need* "big professional set up", these two attributes are the bases for "pro-grade"... then the other stuff (XLR audio inputs, lots of manual controls like zoom, focus, white balance, neutral density filters, shutter speed, aperture, etc) follow with the big glass and imaging sensor system.
On the bottom of your current Sony camcorder, there should be a sticker. On that sticker, there will be a model number. From 10 years ago... that could be either HDR-something or DCR-something. Defining Sony's model numbers plan:
DCR: for camcorders capturing standard definition video at a resolution of 480 horizontal video lines;
HDR: for camcorders capturing up to 1080 horizontal video lines (about 3x standard video resolution). FDR: for camcorders capturing up to 4k (about 4x 1080 HD video resolution).
Assuming we move away from DVD video (standard definition) and to a high definition or ultra-high definition video environment, you would stop using the DVD recorder (perhaps replace with a Blue Ray recorder connected to a computer and a Blue Ray player connected to a HDTV or 4K TV/monitor) and get into high-capacity hard drive storage environments with all the baggage of back-up and file replication along with playback using a computer or perhaps Blue Ray recording and playback... all attached to either a multi-media infrastructure with the video being viewed on a 4k or 1080p HDTV...
By jumping into the high definition video infrastructure environment, you provide for much higher video resolution and allow yourself the potential of "excellent quality video" rather than taking HD or UHD video and stepping it down to standard definition video.
Of the three camcorders on your short list, 2 top out at 1080p video resolution and have relatively small diameter lenses and imaging sensors. The FDR-AX53 does 4k and for a consumer camcorder, has a healthy sized lens diameter and imaging sensor. Because the high-definition video infrastructure can be expensive, take time to acquire and totally revamp your video process flow (and there are different ways to do it), another item comes into play - in this case, each of the three camcorders on your short list can provide composite video (and audio) output so you can continue using you current DVD recorder until you decide to change-out that "post production" environment. The composite audio/video cable is an optional item (not included in the box with the camcorder).
The AX53 has NightShot. In zero visible light, an infrared emitter is built-in (and powered on manually) to capture monochrome video. The two HDR camcorders you listed do not have this feature.
I don't quite know what you mean by "video distortion" - other than under certain conditions, older cameras capturing interlaced video would show artifacts when lots of action was played back. this was a function of action and how alternating lines of video were captured. Since most video is progressive (the entire video frame is captured at one time rather than alternating lines), this sort of "distortion" should no longer happen.
Video noise happens when there is not enough light and common when a camcorder is used in a manner for which it was not designed. Typically, used indoors with poor lighting. This can be resolved by adding light. The upside is that newer equipment has a better tolerance for light so when the combination of a larger diameter lens + larger imaging sensor is used, too, there is a wider "use window" for smaller camcorders. And there is always the STRONG recommendation of adding light (camcorder mounted or just making the entire venue brighter with bright LED video lamps).
Assuming "unclear images" = blur... in consumer camcorders typically used with autofocus on, this is a problems when lighting is poor because that low light causes the camera to do a few things to compensate: open the aperture, increase the video amplification (causes video noise), and slow the shutter speed (causes blur or "ghosting"). Many times, people want the subject to be in focus and the background blurred or the other way around. In both cases, this is "depth of field". Using the combination of aperture and shutter speed, consumer camcorders can provide decent DOF (or no DOF). dSLR (still image capture devices) have the added benefit of interchangeable lens systems and being able to adjust focal length for DOF intensity.
And we can take a break here because I know the above is a lot to digest.
We need to discuss simultaneous video and still image capture...
I have been trying to research the many different camcorders and can't seem to decide. I've always had Sony brand camcorders and really like them. My current camcorder is a Sony Handycam and it's about 10 years old and starting to show signs of failing with color distortion and other video and audio issues. It's been a great camcorder though, but I'm starting to look at replacing it.
I don't need any big professional set up. I'd like something palm size.
I would like the option of taking still shots WHILE taking video. Photo quality doesn't have to be awesome as it would just be for quick snapshots.
Low light quality isn't a deal breaker, but is important.
I want excellent quality video. I hate distortion, noise, and unclear images.
I mainly use a camcorder for family gatherings (indoor and outside) and sporting events (in a gym).
I record all of my camcorder videos onto DVD via a DVD recorder with RCA jacks. I'd really like to find a better way to record onto DVD to not lose any of the quality. Any recommendations?
I've been looking at the Sony HDR-CX455, Sony HDR-CX675, and the Sony FDR-AX53. The 53 seems amazing, but I don't know if the larger size and higher price make it that much better than the other 2. Is it worth it?
Anyway, if you have any opinions on these camcorders or feel there is a better choice for what I use a camcorder for, I would appreciate it.
Thank you so much!!