Yes, it is most likely that your smaller betta in the divided tank is feeling intimidated by the bigger one. Prolonged exposure to this can stress him out, which can make it easier for him to pick up illnesses. Even for the bigger one, the constant flaring may stress him out.
If you're going to continue to keep them in a divided tank, I would suggest strategically placing plants and other decor near the divider so that they can't see each other constantly, or get a divider that is solid. Personally, I wouldn't recommend keeping two male bettas in a divided tank, as I've heard too many stories of one jumping over into the other section. I'm sure it can be done safely though, as long as you're very vigilant about keeping a cover on the tank and making sure there is no space at the top of the divider for one to jump over.
As far as them responding to you, if you have just got them, it may be a while before they get to know you and start to respond to you. Don't be alarmed by that at this point.
I would also recommend getting a heater for their tanks. Bettas are tropical fish and need stable temps in the upper 70's. You can safely use a 25-watt heater in a tank 2 gallons and up. I have a 25-watt heater in my 2.5 gallon and it works great. Don't scrimp on heaters though; make sure you get a good one, and definitely one that has an internal thermostat that you can set. Anything less than 2 gallons, you can't safely use a heater, so I don't recommend keeping your betta in anything less than a 2 gallon tank.
Bettas are top dwellers, so for them to hang around near the top is normal. However, if they don't seem very active and just sit for long periods of time, it could be because they are too cold. (another reason to get a heater) You'll notice a drastic difference in your bettas' activity level if you keep their temperatures stable and warm. Also, they do like interesting things in their tank, so put some things for them to swim through and hide in. You can of course use any of the aquarium decor you see in stores, but make sure they don't have sharp edges anywhere for them to rip their fins. Some people get creative and use little terra cotta pots on their side as a hiding place, or even hamster tubes, parakeet ladders, etc. Make sure everything is washed thoroughly in water (no soap) before using in your tank.
Bettas that you get at the pet store will come in all different sizes and colors. And not all are of good stock, so that's why you might find some that are rather drab looking. I don't think this means they are any less healthy than the others, but who knows!
Here are some good sites to check out for all the information you need on caring for bettas:
bettatalk.com healthybetta.com nippyfish.net And of course, you can always ask questions here on this forum.
Hope this was helpful.
