I can tell you right off the bat that Black Ops 2 is more of the same and probably isn't that different from it's earlier installments which come out yearly.
Halo 4 on the other hand is a brand new trilogy that kicks off with Halo's main protagonist Master Chief and his relation with A.I. Cortana. The campaign is about 7-9 hours long depending on difficulty and can be played co-op with friends online and offline.
The graphics are phenomenal on the Xbox 360 and really seems to push the system to it's limits. The scope of some levels are your typical Halo stuff but keeping that same scope arguably with better visuals and sound effects is a big feat. Of course this isn't no Killzone or Uncharted but it can hold it's own against some of the best looking games this gen.
Speaking of sounds, the piercing shots of the DMR and Battle rifle has improved and sound crisp in Halo 4. The AR sounds much beefier and the rumble feature in your controller enhances the feel of shooting. Everything sounds much more lifelike and realistic.
Minor issues is during cut-scenes the sound effects sound quite muffled and off from everything else that's going on. It's something an audiophile would notice.
Presentation is top notch. No longer are you greeted to a cold world where you feel like a robot shooting aliens for arbitrary reasons. Master Chief comes alive in this installment and the quality of the scenes between him and Cortana is beautiful so to speak. What used to seem like boring characters and non existent personalities is gone and is replaced with people that are alive.
The CG cut-scenes are breathtaking as are the real time cut-scenes. Emotions and life come out of the people on Infinity. Definitely the best halo presentation wise.
Gameplay is quality halo FPS gameplay nuff' said.
MP has been codified a bit as seen in Infinity Slayer. Ordinance drops which seems like an umbrella term for Killstreaks are here granting you power weapons and player attribute boosts temporarily.
Instant Respawns and Kill cams are also in halo. Instant respawning makes for a much faster and frantic deathmatch experience.
Loadouts are now customizable with armor abilties, tactical and support upgrades which are not fairly powerful and is merely an extra layer over the core gameplay. The core gameplay is still intact though the maps can be a bit biased towards DMR usage.
No longer can you fare off in CQC in Halo as people have clung to their faithful DMR in fear of their K/D. If you want to stay alive on the battlefield, equip your DMR and take some shots-headshots to be precise.
Now for Black Ops 2 just play MW3 and BO1 and you won't miss much. Black Ops 2 is probably not even a new game but is merely a DLC map pack with a new skin masquerading as a new entry. I'm sure you'll be perturbed in the near future if you hear that Black Ops 2 content is reskinned black ops 1 content.