First, a few important facts about the DVX and HVX: the HVX has a true 16:9 chip and HD formats always record a 16:9 anamorphic (squeeze) image. The DVX has a 4:3 shaped chip and will only shoot SD.
Squeeze uses the whole 16:9 chip on an HVX, and digitally squishes it into a 4:3 stream, also called anamorphic. Good for 16:9 in HD or SD, will need to be 'unsquished' upon edit or output. On the DVX, it is the same except for the chip is 4:3 (the camera digitally squeezes the image before laying it to tape) and the the output is always SD.
4:3 takes a 4:3 shaped portion of the 16:9 chip on the HVX. Good for SD, 4:3 output. Bad for 'future proofing' your productions. On the DVX it is the same, except the chip is 4:3 shaped.
16:9 letterbox uses the whole chip on the HVX, but places it in a 4:3 letterboxed stream (black bars on the top and bottom). Good for SD 16:9 in 4:3 output. On the DVX, it is the same except for the chip is 4:3 shaped.
You will probably on need to make a decision on what mode to shoot in when faced with specific 4:3 SD productions, I would recommend squeeze mode, but all depends on the project. 99% of the time, I shoot HD with the HVX and therefore shoot 16:9 anamorphic (squeeze).