Compressing the source material will yield smaller results but will be more predictable as the file will always contain ZIP headers and other metadata that would possibly make decryption of your file much easier.
Aside from the headers the compressed data it self often has structure; take the Lempel Ziv class of dictionary encoders rely on repeating data to compress. It is just this fact that it is repeating means that you can guess with much higher probability than normal what certain bytes will _not_ be (because longest words that match the dictionary are chosen to tokenised to maximise compression); i.e. bytes that _don't_ match a word suffix in the dictionary will restart the search for a new matching word / token pair.
Having said that the plaintext itself is almost never random; but the key thing does the attacker have any crib that might be used to have a good first guess that can reduce the amount of work required.
So which is more guessable; the semi-structure, at the byte level, of compressed data, or the possible semi-structure of the original plain text? If you are dealing with a protocol that specifies compression (and in particular which compression method) you may have given away part of the game.
One way is to "bump up" the entropy and add "chaff" to the compressed stream before encryption; i.e. add some entropy but less than what would be less than the amount saved through compression. My gut feel is that the efficacy of this would vary depending on plaintext, compression method, and encryption method. You also run the risk of side channel analysis via CPU, RAM, power usage etc.
What they can predict if they find some code interfacing with this encrypted file is the way it has been stored. It's not much of a long shot to say that if you can identify that it's just a plain zipped file then you're job will be much easier when it comes to reverse engineering this.
That being said, it's still a huge pain in the ass to work with that stuff. I mean, the US government hires some of the worlds best crypto people in the world and they still are sent for a run some times.
It's that the act of decompressing arbitrary data can leak very important information to the attacker.
This depends on the susceptibility of the ciphers to known-plaintext attack; I'm not sure if today there are scenarios where using such ciphers makes sense.