The most realistic of your two choices is the 10-gigatonne nuke.
Accelerating a projectile to the speed of light is an exceptionally difficult task, and is best done over scales of millions or billions of kilometres, or even more. Obviously building a gun with a barrel this long is impractical, regardless of technology. It requires absolutely mindboggling amounts of power, to the point where if you're present in the same solar system as your enemy you'd probably be better off using that power in a large number of much slower weapons.
Thermonuclear warheads on the other hand, even with the original Teller-Ulam design, can be scaled up to more-or-less arbitrary sizes. It might even be possible for us to build a gigatonne nuke today, not that it would be a very useful thing to do.
Such a nuke is probably excessive, though. Let me propose an alternative plan:
Probably should should start by softening up the planetary defenses.
If you've got big lasers, zap everything that looks military from a long way away, if possible. If they've got big lasers in hardened platforms (say, a small moon or asteroid) you should swat them with a long train of big rocks sufficient to overpower any defenses. Use some suitable nuclear engines to boost the rocks into a fast intercept trajectory; you've presumably got decent nuke engineering skills, so orion drives may be entirely practical here.
Finish off everything softer by throwing a load of debris into orbit on inconvenient trajectories, smashing up everything in near-planet space and triggering an ablation cascade. This can be done with missiles. If you've got big lasers, they might be a cleaner way of doing the same thing, but really you want space around the enemy world to be extremely hostile to anything coming off the surface... it is easier for you to drop heavily armoured things into a gravity well than it is for them to fly them out, after all.
Once that's done, drop a cloud of nuclear warheads of moderate size (megatonnes, not gigatonnes), possibly armoured in nice big lumps of rock, and detonate them at the edge of the atmosphere. This causes massive high-altitude electromagnetic pulses. Note that antimatter warheads would be more effective than fission/fusion here, if you have them, because they produce a higher proportion of gamma rays in their blast even at the same overall yield. This will fry all sorts of electronic and electrical things on the surface, including power grids, and toast any electronics still functioning in lower orbits.
Finish off with a sustained asteroid bombardment, focussing on areas of known deep fortification. Keep this up for as long as you can be bothered; the more rocks the better. Spice things up a little by including some salted bombs to produce deadly and long-lasting nuclear fallout, to make sure that cracks in bunkers become lethal and to discourage anyone venturing out once the dust has settled.
When you go home, leave a bunch of observation platforms in high orbit to see if anything stirs on the surface. You should probably park a load of spare rocks and warheads with re-entry engines up there too for a swift automated response, in case it takes too long for human verification. Better safe than sorry!