Both nuclear and thermonuclear weapons are just burning of nuclear or thermonuclear fuel by means of fission or fusion. It is when they are small, they give explosions. Huge devices will just burn, violently, but still burn. Technology level doesn't matter if you want to destroy a planet, you need a huge amount of energy.
I strongely suspect that the beam weapons would be much more damaging to a planet then the AOE. The AOE would just torch the atmosphere, burning it off and disrupting the weather patterns and biosphere, like we see on Reschard. But the beam DDs? Those would probably punch through the crust into the mantle, sending a gout of planetary material spewing out into space to rain down on the planet. It could even critically lose stability and fracture entirely, which would pretty much doom the whole world, basically like Seyllin.
Planets are bubbles of molten rock with tiny crust, flying in space. They are more liquid or 'rubber' than planetary material in our sense. They has huge gravity to hold it together. Your beam weapon will just pierce it like a needle, but you can't 'fracture' a planet entirely this way. What happened in Seyllin was just a solar burst of huge energy, it was AOE and it literally blown planet apart.
Back when Amarr were still "alone" in space, they did nuke Starkmanir Prime. (Substitute "nuke" to purging nearly all life via orbital bombardment.)
Constant carpet bombing is indeed a way to obliterate life on a planet. Even during WWII carpet bombing a city was way more devastating than just blowing a nuke. Just note, that this needs continuous action, quite a number of ships with lots of charges, it's not like 'one device'. Also, you only 'scratch' surface of a planet, but you still cant destroy the planet itself.