The Khemrian Warsphinx is effectively an infantry masher. It is accompanied by four Tomb Guard riding in the Howdah, all of which have the Killing Blow Special Rule. The Warsphinx itself has four attacks at Strength 5, which is more than enough to splatter bits of lightly armoured troops all over the battlefield. However, it can exchange all its attacks for one Thundercrush Attack. As you've probably guessed, this will be very painful for the unlucky troops standing in front of the Warsphinx. If the attack hits, you get to place a small template over the unit, roll loads of dice to wound them all and then do a small celebratory ritual while your opponent takes off a couple of ranks of models. And then you can Thunderstomp them, just for good measure. Against infantry on a 20mm base you can potentially kill 31 models (that's 21 under the template, 6 from the Thunderstomp and four from the crew). Oh, I nearly forgot, it also causes Terror, just in case it wasn't scary enough.
The Necrosphinx is the monster masher1 of the Tomb Kings army. It has the Killing Blow rule and the Decapitating Strike rule. This means that one of its attacks every turn is at Strength 10 with Heroic Killing Blow. This gives the Necrosphinx a good chance of killing enemy monsters outright with a single sweep of his blade (and his blades are big). If worst comes to worst and he doesn't kill the monster, you'll be safe in the knowledge that he will have given it a good kicking anyway. Few monsters will survive two turns against the Necrosphinx and even fewer will have the strength to retaliate. If the enemy doesn't have any monsters then, as mentioned earlier, they'll probably have big guns instead. The Necrosphinx can fly, so dealing with pesky cannons hiding at the back of the battlefield won't be too hard for it either.
I also include that the war sphinx can get poisoned attacks and a breath weapon, both are toughness 8 and have the possibility to get regen from a hero character, or a 5+ ward from a spell.
All this taken straight from GW info