It's impossible to know the behaviour at a current that is not the specified operating point if there's no datasheet containing an "intensity over I_f" graph – if this is of concern to you, buy LEDs that come with such a datasheet.
Yet another thing I'd like to point out that you don't say anything about your 300mA supply – it might look that an LED that is more efficient at 300mA would be the power-efficient choice, but if it happens to have a lower forward voltage at that current (is there at least an I/U graph?), you'll just "burn" that additional energy (voltage = energy per charge) in a linear regulator.
Now, it's really impossible to tell what kind of regulator you have picked there – yes, this looks a bit like the mains voltage gets rectified on the input side, and then chopped up and downconverted by the transformer type thingie there, but I can't tell the least about how exact the current regulation is (but I do have a hunch that without any secondary side sensing, it's not going to be that exact) or how efficient the conversion. So: if you're at all concerned about operational specifics of your LED system, this is not the supply of your choice.
Generally, people will sell their LEDs at the point at which they produce the maximal amount of light without thermal damage (or without exhaustion of recombination opportunities in the semiconductor), and that will be pretty close to the point of maximum efficiency. So, if you want to drive an LED specified for 700mA at 3.3V with less than its maximum power, you typically use PWM to switch it off and on with a configurable duty cycle, driving it at an "efficient" 700mA when on.
Best Answer
This is a bad way to control LEDs. For a start you have them all in parallel - have you done no research at all about LEDs? LEDs need individual current limiting/sharing resistors when placed in parallel or one of them hogs all the current and blows up after a short while then, the current that was to be shared among 4 LEDs is now inflicted on three and, the one that has a slightly lower forward volt drop, takes most of that current and blows.
You can see where this is going - basically after a few minutes or seconds you have no more working LEDs.
You have a 12 V supply and four LEDs which I assume to be standard 2V, 20mA types. So, put them all in series and calculate a current limiting resistor to go in series with them.
If you want to control LED current to control brightness then try googling current sources like this one: -
Varying R2 can give you some control on brightness. Of course you could consider a more elegant solution involving a proper LED control chip: -