Progressive plasma and LCD TV's have powerful de-interlacers built into them, they effectively take the 480i60 image and upscale, and interpolate it into a 480p60 image, in real-time, there is a delay in the picture because of this, and the sound has to be delayed to match - it is quite noticeable when playing rhythm action games on consoles (like Guitar Hero).
Some do it better than others, and some don't do it at all (discard 1 field to make a 240p30 image, and blend).
The same is true of 1080i60 images being turned into 720p60 or 1080p60 by HDTV's, again, some do it badly, or not at all.
What I do on a computer, is use compressor to take i60 sequences and use the advanced format conversion to set the frame controls up to create a p60 sequence, for viewing on a monitor. It takes a long time to do, but looks pretty decent, and still maintains the fluid movement I expect from video (60 updates per second).
For instance, taking 1080i60 HDV and making 720p60 DVCProHD seems to work quite well.