Same number of dots between 1080i and 1080p, it's just only half are updated at a time with 1080i. Complicating matters further, 1080i is refreshed at 60hz while 1080p is only standardized at up to 30 fps due to bandwidth limitations. So it's only "do you want half of your screen updated twice as often," and not like 480i SDTV vs. 480p, which share the same max refresh rate.
Plus it all depends on your source. If you have an analog 1080p player like an Xbox 360 OR your 1080p TV is less than six months old (unbelievably, older Tvs capable of displaying 1080p were not able to receive 1080p through their HDMI inputs) then you may watch a HD-DVD in full 1080p. Or if you hook up your PC to a 1080p TV you can indeed use your desktop in true 1080p.
No cable, satellite, or broadcast provider currently transmits in 1080p, so it is either uprezzed (how it looks when scaled depends on the algorithm used, but never looks as good as true high resolution) or deinterlaced from 1080i (which brings all the same motion artifact problems as going from 480i SDTV to 480p did).
Yes, 1080p is the future, but by the time the future rolls around, a way to make your old TV incompatible will have been found yet again.