Google-sheets – Conditional formatting formulas in Google Sheets

As pnuts suggested, an Apps Script is currently the only way to do this. Here is how one can paint column B the same colors as column A:

var sheet = SpreadsheetApp.getActiveSheet();
sheet.getRange("B2:B").setBackgrounds(sheet.getRange("A2:A").getBackgrounds());

However, you probably want these colors to remain in sync if changes are made to column A. This calls for an onEdit trigger, in which the function checks that the edit was made to column A of a certain sheet, and repaints if necessary.

function onEdit(e) {
  if (e.range.getColumn() == 1 && e.range.getSheet().getSheetName() == "Sheet1") {
    var sheet = SpreadsheetApp.getActiveSheet();
    sheet.getRange("B2:B").setBackgrounds(sheet.getRange("A2:A").getBackgrounds());
  }
}

This script tracks column A (== 1 is its number) of the sheet named "Sheet1".

UPDATE FROM COMMENTS:

You need 3 custom format settings, all applide to the range B3:B. The First is set to

Format cells if...     Cell is empty
and the fill is set to None

The second and third are Custom Formula where the Formula are:

For red:

=B4<B3

and for green:

=B4>B3

OLD INFO FOR Comments

You need 2 conditional format rules. Both applied to cells B2:B, with Custom formula is selected. In the first, set the formula to:

=B1<B2

and set the color to the Red you want to see. In the second, change the formula to

=B1>B2

and select the green color you wish.