Cheating is breaking a boundary or rule defined by both partners in the relationship. You snooped on her phone, that was a boundary of hers that you crossed, she went behind your back to flirt with another man, that was a boundary of yours that she crossed.

I would consider both offenses equally terrible. I'd break up with someone if they snooped through my phone without permission, and I'd also break up with someone who was flirting with others while in a relationship.