Translation:This box is not as big as the other one.
Like I said, it is correct but it is awkward English. Common usage is "as big as", or "as small as", or "it is not as wide as". Native speakers would never say "it is not so big as" They would say "it is not as big as".
The construction is "as adjective as". You can say something or someone is not so bad, or not so rich, etc, but for comparisons you say "not as rich/big/small as"
Others here disagree with you. What is awkward English is the misuse of like to introduce a clause (subject + verb).
Yes, tão/quanto and tão/como are interchangeable, but the first one is used much more often with "adjectives". (Minha casa é tão grande quanto a sua - as...as). As much + noncount noun + as = tanto(a) ... quanto / as many + count noun + as = tantos(as) ... quanto.
este/esta = this. This extends to their conjugation to prepositions like De (i.e. deste/desta) Em (neste/nesta). esse/essa = that. They are conjugated in exactly the same way as above. All have a plural form (just add 's'). There also exist demonstratives for 'that' for objects not in sight. (aquilo, aquela) which are combined with De and Em in the same way as the este(s)/esse(s) esta(s)/essa(s) demonstratives. Hope this helps.
This whole section is so annoying, I know what it means but it keeps making me re-do it on technicalities like 'this/ that' or it doesn't accept a perfectly reasonable answer. please keep reporting the correct versions, this is unbearable, hopefully for others it will become better.