Possibly it depends on your TV, its ability to change the format you give it and its native resolution. With some TVs image manipulation it achieves is better than that can be obtained by a set top box and with other TVs visa-versa. Some TVs/boxes may achieve a downsize by throwing away information and an up-scale by duplicating information while other TVs/boxes may use more sophisticated algorithms.
The difference between 1080i and 1080p when the input source is 1080i may just be a duplication of line information. The TV may be doing similar with 1080i so you wouldn't see any difference.
Not everyone has a 1080 line resolution TV. Some people may have screens with 720 line resolution and others with resolutions based on PC monitors (non-standard TV formats). Some people have their TVs set to over scan which also requires a resolution change. The fewer image resolution changes in the chain from your box to the TVs screen then more chance of a better picture.
In the context of this thread the bigger the number doesn't always mean the better picture. Sometimes it may be better to set the AV settings to the screen resolution of the TV and let the box do the conversions and for other TVs let the TV do the conversion.