You only get the benefit once. It's like having Cathedrals + Mikes, Granary + Pyramids, Hydro + Hoover, etc. The wonder gives the effect of having the improvement. If you've got both, just sell off the improvement for gold.
The benefit of the Wonder over the improvement is that you pay no maintenence for the "free" improvement in each city. If you lose the city with the Wonder you lose all those free city improvements at once - they will reappear as build options on your list suddenly, and if you were relying on Mikes or Hoover you will see sudden unhappiness or drop in production.
Some effects are cumulative, ie. you need a Factory to get any benefit from Hoover in each city. Not sure about needing Library or University to get SETI benefit. Definitely need Temples to get benefit from Oracle. AdamSmith only benefits if you have lots of 1g-maintenence improvements.
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