Difference between 3x1w and 1x3w power supply?
3x1 permits flexible drive design if it comes with 6 pins.
The design can be such as 330mA to 350 in series or ~ 1A in parallel.
Warning : If you buy cheap LEDs online without detailed datasheets, you can expect them to be offspec in some way. Such as CCT, CRI or efficacy etc.   That's why they are cheap.
Instead of 1x3 , which has only one option. for current and voltage , whatever it may be , which may be series or parallel depending on supplier.
Side Notes.
Power LEDs in datasheets are often not rated by Watts as the dominant characteristic, as this is critically dependant on the user's thermal heatsink design.

Rather they are specified with V vs I so a 3W LED is kind of an old way of specifying LED's.

They make power LED's in arrays now with options for 20mA up to 110Vdc for a 2W range or 200mA and arrays of &gt;100W are now possible but demand  critical mechanical thermal skills ( applying Ohm's Law to series Thermal Resistance )

In fact all array LED's are moving towards higher voltage series strings even over 100 V in order to reduce conduction losses with high current drive shunt LEDs and with lower currents achieve higher lumens/watt.

Since they come from the same epitaxial wafer, the V, I characteristics are perfectly matched which is important for parallel operation without the need for small series R's added.


example
Here is a 1x3 or a &quot;3S1P array&quot; with a Vf=63Vtyp @20mA made of about 21 series LEDs but shown as three LED's on chip. Thus permits low current, low cost AC-DC CC supplies.
Although only implied I assume internally the chips is wired as 7S+7S+7S for process or internal design reasons not given.


The 5050 chip comes in many ratings and is common for Ledstrips to be only 1S1P, but for powerbars etc , this may be popular due low current at high Vdc in a tiny chip for 1260mW package rating, which is higher than most in this size with a 4x4 chip in a 5.0x5.0mm package, hence the name 5050.
http://www.seoulsemicon.com/_upload/Goods_Spec/Specification_SAW8LH0A(0).pdf