In Numbers 12v6 God specifically declares that he will communicate with his prophets via both dreams and visions and we find Him using both throughout Old and New Testaments. The distinction between them, at its simplest, is that dreams come when asleep and visions come when awake. Yet this simple distinction may obscure a hidden subtlety that a dream works in the absence of an alert rational mind, a vision works with the human mind. If this is believed then in accordance with 1Co 14:15 we should probably accept that a vision is considered 'superior' to a dream as a method of revelation.
Young's Concordance shows 116 references to dreams in the Old Testament, 52 of these are in Genesis, 29 in Daniel. Yet there are really only 14 specific dreams recorded in the Old Testament, again the majority in Genesis, then Daniel. In the intervening 1000 years we only find two, one given to the Midianites (Jg 7:13-14) and one to Solomon (1 Ki 3:5). In the New Testament we find six specific dreams, all in Matthew: five in the first two chapters and Herod's wife in Mt 27:19.
The striking feature of these statistics is that most of the dreams appeared at the commencement of an era. Genesis obviously covers the patriarchal era, Daniel covers the commencement of the time of the Gentiles, and the early chapters of Matthew clearly cover the coming of the Lord. One might infer from this that dreams come when there is a lack of establishment in things of God.
The other interesting feature of dreams appears once we analyze who received them. We find that whilst God certainly communicated to his own people with dreams he also used dreams to communicate with the heathen. Notable examples are Pharaoh (Ge 41:1-8), Abimelech (Ge 20:3-7), Pharaoh's chief butler and baker (Ge 40:5), the Midianites (Jg 7:13), Nebuchadnezzar (Da 2:1; 4:10,18), the wise men from the east (Mt 2:12), and Pilate's wife (Mt 27:19).
It is interesting too that the interpretation of the dream often was not given to the dreamer and in many cases was given to a Hebrew even if the dream went to a gentile.
I think this shows that an advantage of dreams, from God's perspective, is that they overcome that natural tendency of man to want to ignore God. Job 33:14-17 gives a very interesting insight into this. It says that God will use dreams (and night visions) to speak to someone multiple times, he will open their ears, seal their instruction, turn them from their way and reduce their pride. Again the irrational nature of the dream is ideally suited to dislodge man from his state of complacency (e.g. Dan 2:3)
The expression 'vision' probably originally referred to a prophetic gift of second sight. Examples of this were Samuel in 1 Sa 9:19,20 where he could 'see into' the life of Saul. Also 2 Ki 5:26 where Elisha is able to follow Gehazi 'in heart' and see what he did.
The American Tract Society Dictionary and Easton's focus upon visions as vivid apparitions, thinking of such classic examples as Isaiah 6, the Lord in his temple; Ezekiel 1, the Lord on his throne; Daniel 8, the ram and the goat or even the vision of Zacharias in Lu 1:22. In at least some of these apparitions the visionary would be mentally moved by the experience, some even suggesting that Ezekiel, for example, went into an ecstatic trance. Peter's vision in Acts 10 was certainly accompanied by a trance (Acts 11:5).
We find however that there are instances of visions that are simpler, more mundane and possibly even triggered by normal daily stimuli. For example Amos in Ch 8:1 was shown a basked of summer fruit. Similarly in Ch 1:11 Jeremiah was shown an almond tree. Whilst God clearly could have transported Amos or Jeremiah into a trance to see these items I don't believe he had to.
One thing we additionally see of visions is that they are important. A feature of the time before Samuel, woefully recorded, is that it was a time of no open vision (1 Sa 3:1). The writer of Proverbs is even more brutal when he states that 'where there is no vision the people perish!.'
This leads us to the inevitable question - are dreams and visions used of God today? The first note of caution actually comes from the Old Testament. The general populace was expressly forbidden from observing dreams although they could ask the high priest what they meant. Indeed even if a prophet arose (or dreamer of dreams), if his dreams didn't come to pass or didn't comply with established doctrine he was to be put to death (De 13:1-5). The New Testament doesn't explicitly comment on the issue although 1Co 13:8-10 possibly sheds some light. Those verses suggest that when 'that which is perfect' is come then other forms of divine communication will cease. A good interpretation of that the complete Bible obviates the need for further revelation.
So, in general, it appears that dreams can go to anyone and they dig beneath the conscious of the hearer to make them aware of something they would usually choose to ignore. Visions more frequently go to God's people who are doing his will. As always we must beware of generalities. One striking vision (Num 24:4) went to Balaam; Solomon was sent a dream yet was the author of a huge chunk of scripture. Even Daniel received both dreams and visions (Dan 7:1, Dan 8:1). The real lesson must surely be that God communicates, in each case he is the instigator of the communication and he is thus able to choose the medium. As ever, our duty is to be ready and willing to listen, God will ensure that we are able.