If you have alot of plants/decor - he will probably be a bit more active then in a tank with just one tiny plant and a cave. However you can also add in some other fish to a 10G - corys are a popular choice but they need a group of 6? to feel secure. Snails are pretty neat too and shrimp but they may become snacks. Personally, I like snails myself but some are hermaphroites and will reproduce rather quickly. Others need a male and female and will lay a clutch of eggs while others will give birth to one live snail per day for several days. They poop alot though so a gravel vacume is a must if you dont already have one. They are pretty cheap - about $10 or so?
If I was doing 1 betta in a 10G, I would have 1 section of it with alot of silk or real plants - like a forest and have the other side more open with his house/cave/ect.
I have my 10G's divided 3 ways -so 3 males per tank