Whichever side you sail keep well clear of the central shipping lanes regardless of whether there is a TSS in that area or not. Essentially that means, sail fairly close in to one side or the other* - cross over only as if you were a pedestrian on a major highway. In my experience there's not much to choose between the two sides regarding other traffic, though the English side is a little easier in terms of tides.
This is specially true at the eastern end, the Dover Straight. You will never believe the amount of traffic not only going through but also channel ferries crossing. That having been said, I used to cross over from my home port of Dover to France at least half a dozen times each year, and can't remember a serious incident involving a yacht for many years until the loss of the Ouzo in 2006 (see http://www.maib.gov.uk/publications/...2007/ouzo.cfm)
*For some reason the majority of ships hug the outside margin of TSS's, while just outside there can be coastal traffic going the other way.