Angie, there are a few things wrong with the set-up. First off, though, how long have you had both anoles?
Either an adult Green anole or an adult Brown anole should be housed in about a 20-gallon tank, alone. A 16-gallon should still be fine for one anole, but not two!
Second, Green anoles and Brown anoles do not get along fine. Brown anoles are extremely territorial and Green anoles are easily stressed, as you can see. If your Brown anole is nice to your Green anole, that could be a hint that your Brown is actually just sick. Further, most Browns and Greens are wild caught and putting the two together is just making them share any parasites the other might not have. Also, generally, Brown anoles thrive and warmer and more humid conditions than Green anoles, and don't naturally share any of the same habitats.
When a Green anole stays brown, the first things you should look at are the temperatures, hiding spots, and UVB coming from your lamp. 90*F around the tank is not appropriate, you need about a 90*F basking area with cooler surroundings for the Green and a 95*F basking area with cooler surroundings (but not too cool) for the Brown. Brown anoles need hiding spots, but they're comfortable with just a little. Green anoles, however, need very lush and green surroundings with many hiding spots to feel comfortable. Also, when was the last time you changed their UVA-UVB bulb? What's the wattage on it and what type of bulb are you using? Another thing--what's the humidity?
If your anoles don't seem very active, something is wrong. If your Green anole lets you hold it, something is wrong with it. Yes, I'd take them both to a vet and get fecals done. Parasites are easy to treat in most cases, but can be silent killers, especially if an animal is stressed.
Good luck with your anoles and let us know how it goes. If you care about them, however, I'd move them each into their own, specialized enclosures. While the two species do, unnaturally, live together in parts of Florida, they inhabit different regions of the habitat where they encounter different conditions.
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Got hips like Cinderella / Must be having a good shame / Talking sweet about nothing / Cookie I think you're Tame 