If you have a 1080i TV, that means you have a CRT TV, since only CRT TVs interlace the picture.
If you have an LCD TV, its 720p, and capable of accepting a 1080i signal, but it’s not really putting out a 1080i picture. It downconverts any 1080 signal to 720p. Look at the native resolution. If it’s not 1920xsomething, it’s not 1080 anything.
If you have a CRT that really has a 1080i picture, the question is whether it’s capable of accepting a 1080p signal at all. Most likely, you will have a 720i picture, since older HDTVs couldn’t handle a 1080p signal.
As for the picture quality, if the screen is under 40" diagonal, you won’t notice the difference between 1080i and 720i on most content, and if your TV is capable of accepting a 1080p signal, you won’t notice the difference between 1080p and 1080i at all, since it will always be 1080i.