Hi Jonathan
I'm a little late in adding to this thread as I think most of the guys have more than clarified your original question and I agree with all of their comments that in the main CS are compatible with Britains and Conte. However, for what it's worth I'll just add a little more detail on a few of the CS sets.
Their first series of Reb infantry and the Iron Brigade were somewhat "taller" than either Britains or Conte and therefore quite noticable when placed alongside them. I have to admit they were not amongst my favourite figures for a whole host of reasons and I ended up converting and repainting all of them but obviously could not do much with the height. But their Union & Confederate artillery crews released about the same time are something else and very compatible in height with Britains etc. They are still my favourite gunners by far and I have most of the other companies artillery releases. The action poses, the stance of the figures, the perfect drabness of their uniforms, the gunnery officer barking out "Fire" are simply a joy to work with-I ended up buying 3 sets of each and have never regretted it.
I have attached a rejected shot that I took for one of my dios that gives you a good idea of scale against Conte/Old & New Britain's and the Reb CS artillery crews. As they are all together in the picture it might just help to confirm what the rest of the guys have already posted. The front line gunners are all CS releases except third from left which is Britains-back lines are a mix of WB & Conte
The CS ACW series that followed their initial sets improved with each release culminating in their latest Mosby set which are some of the best mounted action figures in my collection-so far.
Hope that helps
As an aside which has more than suprised me is you, an inhabitant of London, who is mildly interested in The American Civil War????? Holy Cow! and there was me thinking I was the only Blue & Grey unicorn in the whole of the UK
Reb