Difference between IRF520 and IRLZ44N?
You should look at the I-V curves specified for the device.

The first plot refers to IRF520. As you can see, you need at least 4.5V on the gate in order to get a current just a bit higher than 1A. With 3.3V the current could be even lower than 1A. (I can't tell from the graph, but I'm quite sure this device isn't going to work with your setup).



In the case of IRLZ44N you are luckier. With 3V you can get more than 10A (as long as V_DS is sufficiently high). The recommendation was good. Pick this device instead of the other one.