Individual amperage on each rail is very important. In your example, the 350W unit offers more power on other rails, and will be no better than the 300W unit if what you need is more power on the 12V rail.
It's a common situation, cheap PSUs often supply more voltage on the 3.3V and 5V rails which aren't used as much nowadays so that the total wattage is larger, which fools people into buying them.
When buying a new PSU, the most important thing is the reliability and quality. This can be determined by first checking the manufacturer and OEM, and by reading reliable reviews of the unit. Customer reviews don't count for much.
Also, welcome to the forums.