Neither alloy is particularly bright white so the white gold seen in most shops is plated in rhodium, this is a very bright shiny white (more like silver). As it is plate (a thin layer placed over the solid metal.) this will wear through and need to be replaced on a regular basis. Underneath the plate 9ct and 18ct white gold are very different.
9ct white is a soft, warm white. it's a very flattering colour and a warmer alternative to silver. 9ct gold can tarnish over time if not worn, but this isn't an issue if pieces are for everyday wear.
18ct white gold often contains palladium, and without the rhodium is a similar colour to platinum or palladium but with a browner tinge.
As standard I do not plate my white gold, in particular I have found 9ct white is a very popular option for wedding jewellery as it's such a flattering colour for a white metal, much gentler than the other options.
Personally I think if you are considering 18ct white gold you should look at palladium, which is slightly less expensive and doesn't require the plating. However as palladium is quite new it isn't as widely available as white gold.
Although platinum is now popular for jewellery and easily the most expensive option it's properties were not well understood until quite recently.
Platinum is a very dense and inert metal, very scientific sounding but it means that the metal is tougher and wears less than gold, and also that it doesn't tarnish in air as silver does. It is a good, although expensive option for wedding bands as it lasts very well.
Platinum is very rare and only a small amount is mined every year, so depending on industrial needs the price can be quite volatile.
Platinum is so tough it can wear through other metal if placed next to it, so it isn't generally advised to wear a gold band next to a platinum ring.
Palladium wedding rings
Palladium is a similar metal to platinum, although less dense and easier for jewellers to work with it has similar properties.
Discovered in 1802, palladium is relatively new to the jewellery market, although it has been used for some time to make white gold. The UK Assay Office (See my gold, carats and colours page for a bit more info on hallmarking.) have introduced hallmarking for palladium in the last few years.
Palladium at the moment is less expensive than platinum, with a very similar look so is a good option for heavier bands which could be prohibitively expensive in platinum.
Palladium is sold in the UK in 2 different purities, 950 and 500. 950 is simply 95% palladium and 500 is 50%. Not everywhere advertises which version they are selling so if you are comparing prices it's important to be clear which version you are being offered, There will be a difference in the durability of the 2 different versions.