I've driven both the cars, I'll personally say that the Altis is way better. It is more comfortable and comparatively better on fuel despite being a 1.8. Though the build quality may not be as good as the Civic's but they do last quite a while as they are quite tough. It has a better interior, much more open space, better sound system (equipped with 6 speakers) and has airbags as well. In your case, if you get a civic, you will end up with a car that is 10 years old and it is gonna be quite an issue for you. And it's very rare that you find a Civic 02' in good condition these days. Even if you do, when you're about to sell it, it won't fetch as much as the 06' Altis. Altis may not have the resale value of an XLi or a GLi but it's still better than that of a Civic.
As far as performance is concerned, the Altis would annihilate the 1.6 Civic in a 'drag'. The 1zz-Fe is quite a powerful motor. Therefore the Altis is a very quick car, with loads of torque in the low and mid region. The brakes are good too and the suspension absorbs bumps quite well.
As far as looks are concerned, I find the Corolla much better. I personally dislike the look of the 7th generation Civic. Prefer the 6th Generation more. If you go for a metallic grey color, tint out the windows a bit and add a decent set of rims, you would love it.
So, definitely go for the Altis.