JPEG is a "lossy" file format. It throws away (loses) image detail. The more you compress a file the more detail and quality you lose. If you shoot to JPEG in camera then immediately you have thrown away data before you can get your hands on the file for any further processing. This is one reason that many people prefer to shoot raw rather than JPEG.
A quality setting of 10 means that you are throwing away less of the image data than a quality setting of 8. The file will be (much?) larger but may or may not contain additional useful information. If you have scenes that are devoid of much detail - e.g. the paintwork of a car - then losing detail may not matter a great deal. If you have scenes that contain considerable detail - e.g. a landscape with grass in the foreground and middle ground - then you may wish to preserve as much fine detail as possible.
Noise is really a separate issue altogether and should be dealt with separately. The first question is - what is the caause of the noise? Is it needlessly high ISO? Is it underexposure at capture? The 1D3 is a cracking performer as far as noise is concerned, and all other aspects of IQ. Noise oughtn't to be a problem unless shooting in the most miserable of conditions. The best way to deal with noise is to prevent it occurring in the first place, with proper consideration of exposure settings at the time of capture. The second best way to deal with noise is by using noise reduction settings either within the camera or in software afterwards. IMHO simply increasing JPEG compression is not the right solution to masking noise.
If you want to address noise after capture, in the best way possible, then you will do well to shoot raw and then you leave yourself as much flexibility to fix the noise as you see fit, whether using settings within your raw converter software or using dedicated NR software such as Neat Image, Noise Ninja etc.. But you should always aim to get that exposure correct in the first place.
Can you post an example of a typical problem image, without edits, and with EXIF attached? Then maybe we can offer some further advice. I'll go first....
Here is a shot with my 1D3 at
3200 ISO, 1/60, f/3.5. Flash was used. This was shot raw and has had no edits other than a white balance adjustment and +0.4 exposure in Lightroom. Everything else, including noise reduction and sharpening, is at Lightroom defaults.
Full image....
100% crop....
With some attention to noise reduction in post I'm sure this image could look very smooth indeed, but when viewed at normal levels of magnification rather than 100% the noise is a non issue, even at 3200 ISO.