Yes, going up the chain in headroom amps will give you greater sound quality.
The supreme will sound better than the total airhead, the cosmic will sound better than the supreme, and the cosmic reference will sound better than the cosmic. But each one costs successively more, and the quality increase gets smaller with each jump. The better the product, the lower the price/performance ratio.
Also, if you want portable, remember that while the cosmic is technically 'portable' that it is very heavy, and requires a 4D cell battery pack!! You pay for quality, and not just with money, but with your back, lugging the thing around.
If you want better than what you have, and have got money to burn, then go for one of the bigger headroom amps, it will be everything you like about the total airhead, but MORE. But if you are happy with the total airhead, go ahead and keep it! No pressure to upgrade, the total airhead is a great amp, and with only 3 AAA batteries, its very light and portable. I'm very happy with mine.
peace,
phidauex