1) Can you supply links to the sites that indicate the Sony HDR-CX190, CX210 and CX250 are "not exactly full HD"? The definition of standard definition video is 480 horizontal lines; high definition video is 720 or 1080 horizontal lines. The Sony HDR-CX190, CX210 and CX250 all use AVCHD compression - by definition is high definition. Whether "full" high definition or not might be debatable - but if they are Standard def video as stated, Sony is wide open to false advertising legal issues...
2) The list of requirements you provide is normal... one at a time - other than we really do not know how picky you are... In my opinion - per your requirements:
* full HD: This is merely "1080p" as opposed to 720p or 1080i. Horizontal line count is only one measure that contributes to "video quality". In addition to lighting, the amount of compression applied to the video data as it is written to the storage media plays a huge role. It is easy to be recording 1080p video that looks worse than standard definition video. The 180p is highly compressed; the standard definition video uses low compression.
* low light recording: In order for good "low light recording" the camcorder needs a large lens diameter to allow light into the camcorder; then a large imaging chip (better yet, large 3-chip array commonly referred to as 3CCD or 3CMOS) is needed to deal with what light is allowed in. The camcorders you list are essentially entry-level consumer grade camcorders. Their lens diameter is usually in the 30mm to 37mm range. Most have no threads to mount filters or add-on lenses, so they do not list the spec making it impossible to know their lens diameter. The single imaging chip size is normally in the 1/6" to not-quite 1/4".
As camcorders increase in price, lens diameter and imaging chip size grows. Just setting the expectation: Low light behavior for the list of camcorders you have provided won't be too good. Captured video will be grainy.
* shake stabilzer: Humans were not made to be stable. Either mount the camera to your body, somehow, or use an external steadying device (tripod, rock, chair, shelf...). Optical stabilization works to a point and *some* video editors have a "shake removal" feature (iMovie for Macintosh) - but best practice is to not use the camcorder handheld. One learning challenge I had was understanding that the camcorder is not necessarily the human view. When the camcorder is handheld it is easy to quickly turn the camcorder as the camera-person's attention is drawn elsewhere. One of the last things you want to do is quick-pan the camera and go back and forth between subjects. Professionally, multiple cameras would be used for back and forth cuts. We don't get that luxury, so we compromise.
* good battery life: Get an optional high-capacity battery or two from the camcorder manufacturer. I've read from several folks who decided to spend less $ on the battery from a third party only to find that they caused more problems and were not worth the "savings".
JVC, Panasonic and Samsung all make competitive products in the same price range. The video file types are similar, the amount of compression applied is selectable and similar. AVCHD files are MTS, M2TS or TOD from all.
A big part of video is audio. You make no mention of any audio capabilities/requirements. At a minimum, a mic jack might be preferable. Better yet, a mic jack with manual audio gain control. In the camcorders you listed, most have a mic jack. A couple rely solely on auto audio gain control. Most have a few with at least a "normal" and "attenuator" (for loud audio) settings accessible through the camcorder's menu.
And we assume your computer has the horsepower and storage space to deal with AVCHD compressed video - many cannot. Of course, that assumption is based on the assumption that video editing or playback on a computer is planned. That takes us to the next step of understanding the playback audience (computer, tablet, smartphone/personal media player, video sharing sites, DVD, Blu Ray and knowing there is no single best file, but multiple different files are needed.
I'll take a breath here...
After a long research on camcorders (based on my budget) I have been able to short list the following
Canon Legria HF R306, R36, R37, R38, M506 & M56
Sony CX190, CX210, CX250 CX260
In Sony, except for CX 260 all the others are not exactly full HD (they just use SD and try converting to HD as per some sites)
Therefore, I am confused which brand to chose. The web reviews that I have read give details and specifications of each model but there does not seem to be any specific comparison between various models. Moreover. most sites have technical jargon which I dont understand. All I am looking at is good video recording, full HD, low light recording, shake stabilzer and good battery life at the best possible price. eg. There could be a canon and sony with exactly the same specs and video quality but with a different price. I would definitely go for the lower priced one. For this I need someone to help me chose from the above mentioned camcorders or suggest something equally good in JVC, Panasonic, Samsung, etc.
I do realise that each model has its own specs, pros and cons. But I am looking for someone to help me make a decision as a layman without any technical knowledge who wants to get his moneys worth.
Thanks and Regards