A:  Hello Sam :). Well first off, I want to say "Thank You"  on behalf of your betta, for taking such good care of him. In my experience, a larger tank with better environment can in the end only help your betta's health and spirit. Will he go through a transition period? Probably. He is after all, being introduced to a new surrounding, which to him will be unfamiliar and may seem (at first) somewhat threatening. Will he go into depression? Not necessarily.

I bet you that bettas, in their little heads, think, when are first released in a new tank: "Oh, cool, it's big! But are there any predators in it?". So even if they liked the water, filter, plants etc, they may still act a bit cautious at first. Soon they roam around long enough to realize nothing is hidden behind the intake tube or the rock, or plant and they figure out that they are safe, and act accordingly by taking over the tank and flourishing :). 

Now let's talk about betta depression (wait, let me put my betta psychologist hat on LOL). Dr. Faith says: Betta depression is real. Bettas do go into a depression phase which can last from a few days to a couple weeks when:

• they are removed from the spawning tank after spawning. Here the depression may be due to exhaustion as well as maybe (possibly) (and I'm realllllly going out on a limb here) because of the sudden separation from their fry. Note: You do not have a choice but to separate the male once the fry are free swimming, otherwise he usually ends up eating them. So the separation is a necessary evil and Mr. Betta eventually gets over it (company helps). Not all bettas sulk when removed from spawning tank by the way.

• they are first put in a jar. Bettas that were in a community tanks (grow out tank of young fry that are coming of age, female community tank etc...) and are pulled out of the tank and placed in jars (solitary confinement) may also sulk for a while. Lack of space, stimulation and company is in my opinion the culprit. So make sure they can see other bettas and that their jars are large, or else!

• they first arrive in a new home. Bettas that have just been acquired and moved to a new home may sulk because of the sudden change of environment. Sulking will be more severe if the acclimatizing has been rushed or not done properly, or if the new environment is not adequate (poor water quality, untreated tap water, too small of a jar, no social interaction with other bettas). 

If your new betta is sulking, it may last from a few days to long weeks :((. Extreme cases of depression will involve starvation, meaning Mr. Betta will go on a hunger strike and not eat a nada. This can cause some problem as it weakens the fish and may cause it, on the very long run, to perish. 

What to do when your betta is depressed and sulking:

• make sure Mr. Betta is not sick. Sick bettas and sulking bettas may exhibit similar symptoms, including lying at the top or bottom of tank, not swimming around, not eating, clamped fins. So it is important you make sure your "depressed" betta is not actually a sick betta. Check water parameters, set-up etc... Make sure everything is kosher and that water is clean. 

• add bettamax as a prophylaxis treatment. If the betta is not sick it won't hurt but if he is coming down with something, it will help.

• add vitamins (aquarium vitamins that is, you can get them in liquid form at your local fish store) to his water

• most importantly, provide some sort of visual stimulation to "entertain" Mr. Betta and cheer him up. This is best achieved by putting other bettas next to him so he can see them and interact with them. Don't have other bettas? Try a lava lamp, or other visually stimulating gismos. A simple mirror may very well do the trick for you (never place the mirror inside the tank).

In closing, bettas rarely sulk when they are moved from one tank to another within the same home because the water parameters and life style remain about the same. And for as long as you don't take a betta out of a 20 gal tank to stick it in a small jar, bettas will usually be pretty forgiving of your reorganizing their homes. So I think your fish will be just fine and should actually be more active and happy now than before :). Hope this helped you.