I am a bit confused by the appropriate use of 大约 and 差不多. I have learned to use 差不多 in many cases where I am talking about an approximate amount, value, extent, etc. of something, or speaking about how two things are similar. Would someone be able to provide an explanation differentiating these two words / concepts? Also, is one or the other more common in colloquial usage?
大约 means "approximately", 差不多 means "almost".
大约 is normally used as an adjective or adverb in phrases like:
大约四英尺厚的雪 snow that is approximately 4 feet thick
差不多 can be used in a similar way, but it's more commonly used as an adjective-verb:
这两本书的内容都差不多 these two books' contents are about the same
However, 这两本书的内容都差不多一样 (with 差不多 as an adverb) means the same thing.
The important thing to remember is that 差不多 means almost, but not quite, so two things that are 差不多一样 are not exactly the same. Whereas something like 大约一个小时 could be exactly one hour, although it could also be a bit more or less.
差不多 is also commonly used in a colloquial sense:
差不多了吧 that should do it
In my experience, 大约 is more common in written language. The spoken equivalent is 大概. But that may be a regional thing. 差不多 is very common in colloquial language, mostly in the sense of "about the same" or "good enough" as in the examples above.
The term 差不多 can easily be understood by direct translation. 差（v）＝ differ ， 不多 ＝ not much. Thereby, we can see that it means "not to differ by much" which logically corresponds to almost. In certain context 差不多 and 差点儿 means the same. The same logic applies here also, as 一点儿 means "a little", being the same as "not much".
The word 大约 can best be translated to "approximately". Which then becomes obvious why it is a more formal word than 差不多. As said before its spoken equivalent is 大概 which best is translated to "roughly" and thereby also showing that it is more colloquial.