Driving LEDs: Brightness, efficiency and heat generation
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.