I live in Florida and have spent plenty of time in the woods and the swamps, so I can give a few interesting weather details. I don't know if this will cause you more problems, since you asked for the difference between the two, and problematically, we don't really, actually have real rainforests here, tropical or subtropical, although we do have tropical and subtropical weather ranges in our state. You mentioned Florida specifically, so I can give you an idea of our weather in this area. I have lived in both the tropics here and subtropics.
South Florida: hurricanes, heat.
North Florida, Central Florida: Longer dry season, will reach freezing especially in the middle of the state away from the coast.
--monoculture is present in all of Florida. While there is diversity it's not even close to what you'd find in a rainforest environ, there are also miles and miles here where you will see one type of plant, just DOMINATING--like scrub palms.
--Rainforests are rare. I think the fact that we are built on a limestone base prevents us from having the soil needed to have what you would call the strict definition of a rainforest. The conditions needed for a true rainforest are very specific. We don't have them. There are places that bank on the lack of knowledge for tourism and claim we do but, our canopy just isn't high and dense enough, among other reasons. South Florida and Central Florida does support many South American and rainforest-type critters and plants that could adapt. Many of those have found their way to North Florida. Central and North Florida will freeze, about twice a year.
--Because we don't have the kind of canopy you'd find you can see the light from above, you might actually be able to see our weird, weird weather. In a proper rainforest, everything is filtered because of the canopy. When I say weird, I mean that you can be standing in the rain, and then take a step to your left and be standing in the sun. In Central & North Florida it sometimes hails in the summer at random. It's random enough that it can hail over a house and it never makes the weather channel because it didn't hail anywhere else. The further South you get in the state, the more regular the rain gets. During the rainy season it gets unbearably hot and humid, rains by 3 or 4 pm and then clears up again. Most days, it's about 10 minutes worth of rain. It can rain all day, but that doesn't happen often on its own, unless it's a tropical storm, and we have plenty of those, and hurricanes. Waterspouts also happen if you are near the water. About once or twice a year, in Jacksonville (that's in North Florida). The clockwork rain happens more often in the tropical portion of the state, but this weather happens all over the state (even in the subtropical parts).
--Sometimes it doesn't rain. If it doesn't, things brown up pretty quickly. The further you get from the ocean, the more extreme the weather will get (with the exception of hurricanes, those don't hit there as often) but on a day to day basis, away from the coasts, it gets colder, hotter and the rains last longer and are more severe. Cold in Central Florida, away from the coastline, is a wicked bad thing. When it freezes, it feels terrible because it's humid and cold.
--In parts of South Florida, temperatures get too high to qualify for rainforest status (over 100). Ft. Lauderdale, though, actually falls into the weather & temp range of Tropical Rainforest, only none of the other conditions are really right for it.
--And I will throw in a difference that I have noticed, subtropical & tropical Florida vs. everywhere with real seasons. We are green all the time, except in the winter "dry" season, and even then we are certainly greener than the places up north. The upshot of the constant green is a lack of the vibrant green and springtime color I see up North. (Barring unnatural lawns and golf courses). It's like, up North, all the colors happen in one go, so they are brighter during spring. Flowers are brighter as well. And of course, there is no such thing as fall. The most we will get is one sensitive tree changing. Colors change slightly in Central and North Florida, but by then it's no longer tropical at that point.
--If you are looking at adaptive species of plants pushing their normal range, Florida is the place to study. Central and North Florida is an amazing mix of subtropical, tropic, and there are some environs by springs that some call "rainforests" (think there's one in the Keys as well). The canopy there is much lower, lets in more light and features less diversity. Any picture you see of a Florida "rainforest" will nearly always include sky.
--The Devil's Millhopper in Gainesville, FL is pretty close to the feel of a rainforest, as is Brick City Park in Ocala, FL. Both of these are in central Florida, both of these feature holes cut in the limestone. Within the hole is a small environment. Millhopper has an obvious spring, but Brick City Park is less so. The springs feed water constantly and the enclosed walls keep the temperatures more constant. Brick City Park has lots of Ferns, bamboo and tends to flood a lot. The weather in the area hits the subtropical range you are looking for, and in this very specific & tiny environment, could actually support tropical species, because the place offers some measure of protection from freezing (although it will freeze).
--You might also want to look at Georgia, as that's also considered subtropical, but it very, very different, mainly because of the soil and elevation in places. I have family in GA and found the weather to be more stable and less strange over all. Does freeze quite a bit more, but much of the state is considered subtropical. Here's a link to plants moving up because of weather changes.