I used to live and hike in New Mexico so I can tell you something about the difference.

Bugs are the big downside of camping back east. Ticks and mosquitoes are your companions in the woods. But there are good repellents for mosquitoes. For ticks you will need to treat your clothes with permethrin and also carry something to pick off the ticks at night that get past the chemical.

The humidity takes a little getting used to. You will find that you sweat a lot more for the same temperature and effort level (actually you were sweating before too but it evaporated so quickly you may not have noticed). But the humidity has an upside too. There is no blowing sand in the wind (in New Mexico you can't smile when the wind blows because you get grit on your teeth). Also in the west your tent and socks are always getting full of sand and dirt. Not so back east.

The big difference you will notice is that the day/night temperature fluctuations are much smaller in the east. Not sure if this is due to the elevation or humidity. In the southwestern U.S. a 40 degree differential is common which means a pleasant day turns into a cold night. In the east it is more like 15 to 20 degrees. So for me a "summer bag" means no bag at all. I sleep under a bug net with just my clothes as covering. I'm not sure you need to worry that much about rain. My recollection about the southwest is that rain was infrequent but when it came it came down hard and fast. So if you were prepared for rain (in terms of shelter) in the southwest then you are prepared for rain in the east. But you will find yourself hiking more often in the rain. In the southwest you can "wait until the rain passes". That would be a long wait back east. So "rain gear" means more than a tent or tarp. Better get something to wear on rainy days like a poncho or a rain jacket and pants.

There's lots to like about both places. You will miss the scenic vistas and sunsets of Colorado. But you will really enjoy the lush green of the east, the trails that are completely roofed over by a canopy of trees, and the little creeks and ponds.

Have fun.