Composite means that the brightness and color signals are sent through the same wire (as opposed to S-Video where they are separate.) This means that they have to be separated again somewhere in the chain. Due to the composite signal having limited bandwith, the colour and brightness can often interfere with each other, resulting in visible artifacts such as
dot crawl. Capture devices use something called a comb filter to filter out the signal interference, both the AVT and the es10 have one, but I don't know which is better. The old ATI AIW cards have decent comb filters as well, many of the modern usb devices don't, so it may be worth using the AVT or es10 as a pass-through for this purpose. Alternatively, a some high-end vcrs can also do this on pass-through.
I don't really know much about betacam, so I can't say much about whether there are betamax devices with s-video out, which would be the ideal choice if possible.