Clean sand will filter to about 60 microns. When it gets dirty it will filter to about 30 microns.
Most of what I've read claims sand will filter particles as small as 20-30 microns, cartridges 5-10, and DE 3-5. I don't have the ability or inclination to test that though.
And those claims are not wrong either. New sand that has not smoothed off and is slightly dirty might actually be able to trap particles that are as small as 20 microns. Old sand that is polished probably won't get anything smaller than about 60 microns when it is freshly backwashed. The Reemay polyester material that carts are made out of is usually rated at 20 microns but when it gets dirty and the pores start to get plugged it will filter out much smaller particles and beings to approach DE in effectiveness. DE will filter to about 5 microns but , once again, when dirty can go a bit smaller but this is self limiting because it clogs so easily and then your pressure rises, filtration becomes less effective, and you have to clean the filter so this is more self limiting.
Adding DE 'dirties' the filter and will not produce the 5-6 micron filtration a DE filter will since the DE can and will move between the sand particles.
In my experience, I have seen the DE coat the top of the sand bed down to a very shallow depth (maybe as deep as 5mm) and not move any further through the sand.
Much of the DE will sit on top of the sand but unless you actually stir up the sand bed and look you really don't know how much is between the grains. Also the fact that much of the DE is sitting on top means that it can be disturbed and that larger particles can get past it. You are putting MUCH less DE into a sand filter than you would in a DE filter so the filtering depth of the DE is going to be much less and therefore it's filtering ability much less.
It will improve filter performance of a sand filter to a degree but it no way comes close to the filtration of a DE filter.
I wouldn't claim that it it equates to a DE filter because I just don't know. Intuitively though, it seems that it would get close.
IMHO, you would see a greater benefit with older sand when you add DE. In fact, most of the people who swear by DE in a sand filter are the same ones who say you never have to change your filter sand! (If you've read the threads at PoolForum you know what I'm talking about.)
Also, as sand ages and the facets on the sand become 'polished off' from the erosion of the constant flow of water it becomes less effective at catching particles and it's filtering ability decreases. Sand's biggest plus is that it is the easiest type of filter to maintain. A cartridge will filter to about 20 microns clean and probably below 10 microns when it starts to get dirty and actually approaches DE's effectiveness at filtration, unless the cartridge has been acid washed. Acid washing a cartridge will cause the filter fabric to stretch and the pores in the material will become larger. (A cartridge is, IMHO, much easier to clean than a DE filter, which really should be broken down to be cleaned and not backwashed or bumped, but that is a topic for another thread!) The biggest drawback to a cartridge filter comes when they are undersized and the time between cleanings is very short, an all too common occurrence! Also, as any filter dirties the flow rate will decrease which will make filtration less effective since it will take longer to filter the same amount of water so while you can increase the effectiveness in terms of size of particle filtered there is a diminishing return because it will take more time to filter and 'turnover' the water.
Will the flow actually decrease? Won't the increased resistance be overcome by the increased pressure? (E=IR in electricity is roughly analogous, no?)