They are not the same type of tester and from using both I can tell you the load tester revealed bad batteries that tested ok on a Handheld tester.
Anyway, did you integrate with the Bose system or bypass? Are you using the stock speakers? If they are Bose stock speakers they are usually 2 ohms which is too low for your HU to handle. Does your HU get really hot? Do you have the loudness button turned on?
Edit: your sig indicates you are using your bose speakers. Test them with a DMM, are they 2 ohms? If you are going to use them and they are 2 ohms, get yourself some high power 2 or 4 ohm resistors and wire them in series with the speakers. Or go with a dedicated amp that can handle a 2 ohm load.