These are correct:
(1) I would rather he be honest. 77 for "would rather he be" site:uk.
(2) I would rather he were honest. 84 for "would rather he were site:uk.
(4) I would rather he was honest. 478 for "would rather he was" site:uk
As you can see, in BE at least, the past tense is the most common.
This is wrong:
(3) I would rather he is honest. 45 for "would rather he is " site:uk (but with one sentence repeated a lot of times, so actually 8: "In order to show you the most relevant results, we have omitted some entries very similar to the 8 already displayed.")
The sentences all mean the same thing: he is not honest, and you wish he was. The difference is only in the formality: the first is the most formal, and the last is the least. The first might sound pretentious when used by someone who is not normally formal.
(1) I would rather he be honest. - present subjunctive, used when you wish someone else would do something. You can't say "I would rather I be rich", for example.
(2) I would rather he were honest. "The past subjunctive effectively relates only to the verb to be, where it takes the form were." http://www.tiscali.co.uk/reference/dictionari...
(4) I would rather he was honest. (past tense)