Real plants are generally considered better because not only to they feel more natural to your fish but they also help improve your water quality by removing ammonia straight from your water. They do require a lot of up keep and special lighting but I definitely think theyre worth it
I don't know that much about rainwater v. tap however, but I would guess rainwater would be somewhat unstable and I personally wouldnt use it.
Rainwater will have 0 carbonate hardness. Great for softwater fishies. It will not have any minerals, harmful or beneficial. It will contain dirt and pollutants from the air and the drain system you use to collect it. So unless you are working with some species of fish that requires super soft water, I wouldn't bother with it. The water from the tap is too convenient and with proper conditioning is fine for 90% of the fish we keep.