The main differences between the two breeds are weight, size and leg length.
The similarities are that they are both white, can produce very high milk yields with good butterfat percentage, and are very easy to handle, having a placid, quiet disposition - very well behaved, as goats go!
Other breeds, such as the Toggenburg and British Toggenbury can be very excitable and active, making it difficult to keep them inside the boundaries of their fields or paddocks, and Anglo Nubian goats tend to bleat a lot.
Most British breeds of goat have the 'mountain' shape: when viewed from the side, the line from the shoulders to the rump is almost horizontal. In some cases the shoulders are a little higher than the top of the rump. This gives the goats perfect balance and control on steep slopes, but not a lot of ground clearance to their udders. This shape has come from the influence of the Swiss breeds on British stock.
Goats adapted to shrubland, such as the heavy-milking Murcian goat of Spain has the line rising steeply up from the shoulders to rump giving much better ground clearance to the udder. Of the British breeds, the Anglo Nubian possesses this character and also the British Alpine, to a
rather lesser extent.
These are of Swiss origin and all are descended from imported stock, the majority of which came from the flat fields of Holland. They have short legs and large udders which is fine if they are raised on improved land, but causes problems on rough grazing. Their udders can get damaged and cut by rocks and brambles so it's important to check their udders, even when they are not in milk as any cuts or grazes can cause infection, or even mastitis.
They are capable of some of the very highest milk yields.
Some Saanens are white-skinned and if they are kept in sunny climates they many develop skin cancer, but the dark-skinned Saanens (which are also white-haired) are immune.
The British Saanen
These are of mixed origins and are usually considerably heavier than Saanens. They also have longer legs, which is beneficial if they are kept on rough land. They are just as likely to produce milk yields as high as Saanens but their udders tend to be less shapely and rather 'baggy'.