Both ratings are likely correct.
It used to be common years ago (maybe still is?) for cheap car amplifiers to list peak power not RMS, which usually meant combination of not RMS, one cycle only, and even then still probably fudging a bit.
We could argue semantics but peak or burst power isn't all smoke and mirrors marketing jargon. It all depends on the time duration. Peak for one cycle not so useful. But the LabGruppen and clones have significantly higher burst power than continuous power ratings and that is useful because there is (generally) enough capacitor supply to sustain that for a meaningful period and the output devices can handle it.
Knowing the time duration it can sustain 2700W would be helpful if you're looking to match or exceed that with a replacement. When looking at prosound amps, you will find plenty that have lower continuous output ratings than their burst power. That continuous should match or better the 600W rating (if that is your goal), but the burst will have a lot of variation from brand to brand and model to model.