Yes, they all sound better with the auxiliary verb at the end. You basically have three options:
1. "I am not as smart as he."
Correct grammar (subject case pronoun) but old-fashioned and pretentious. Sounds weird to most people.
2. "I am not as smart as him".
Incorrect grammar (object case pronoun) but widely used. Sounds OK to most people.
3. "I am not as smart as he is".
Fine. Not wrong. Not old-fashioned or pretentious. Not weird. Definitely the best choice.