NCR disadvantages:
1. Barely enough troops to cover Mojave
2. Low morale overall.
- People tend to forget Camp Forlorn Hope - NCR's primary forward camp in the east. Without the Courier's intervention, that camp would have been outrun/deserted anytime because NCR can't spare the men to give them more troops and supplies. If they try to go out and find supplies, Legion would kill them.
3. Not all NCR troops use riot armors, most of them use leather ones like the Legion anyway.
4. Weather, NCR troops usually complain and wish for a nuclear winter - uncomfortable, whereas the Legions are more adapted to the weather.
5. NCR troops are not well-trained. Most of them are conscripts - which is low quality/poorly trained soldiers.
6. Low will, form reason #5.
7. Legion's agents within NCR force feeding informations to Legion (quest I Put a Spell on You, remember he'd almost never have been caught if the Courier hasn't intervened).
8. Chief Hanlon (commanding officer of the NCR expeditionary force into the Mojave region, also highly influential in the Rangers) feeding false information to the NCR force itself, stirs everything up in hope of a resistance to rise against the higher echelons of the NCR military.
9. President Kim Ball would have been assassinated during his speech and visit in Hoover Dam to boost soldiers' morale, which could ultimately kill the troops' morale (will) and makes every Mojave and NCR citizens to doubt their army's power (if you've killed Kim Ball, by the nuke from The Divide or any other means, you'll know).
10. Potential uprisings (high taxes, annex the entire Mojave without asking the people living in it, won't provide protection overall (Primm for an example) etc).
11. General is Oliver (lol obviously).
12. Legion attacked Nipton (the closest town to NCR's border to the Mojave that is heavily guarded) and burned it to the ground without them even knowing it.
13. Powder Gangers.
14. Being used by Mr.House (he opens his Strips to NCR soldiers so he could suck their money lol, of course Mr.House has never fancied these guys), this could also be know from talking to Chief Hanlon.
15. Lower physical strength.
16. Low number. (Of course)
17. No vertiberds to support the war at the Dam.
18. Soldiers are not disciplined (well they are just conscripts after all).

I am sure there are more than this but this'll do.

Legion advantages:
1. High number (higher than the first war, Legion got help this time (they gathered soldiers from all over the region not just the Mojave, slave soldiers from tribes that Lanius conquered or enslaved)). In the area, they got the Omertas, Khans as allies.
2. New Legate (the first war was lost because their Legate got arrogance and think they'll do just fine by outnumbering them so he just orders his troops to use the "men rush" tactic, thus resulted in getting trapped in an explosive town and killed, now he's known as The Burned Man if you played Honest Hearts), that won't happens again.
3. New strategy (#2).
4. Legion is facing a dumb NCR's general (General's Oliver, who I assume think the same thing as Joshua Graham, he stationed a lot of troops at Hoover Dam thinking a lot of troops will do just fine).
5. Multi directional attacks (if you've finished the game, surely you know that if you side with the NCR, the Legion attacks from both the outside and inside Hoover Dam, NCR wouldn't have been able to hold it without the Courier).
6. Loyal troops with high will/trust their leaders/fight to the death.
7. Physical strength/melee advantage.
8. Caesar's a natural military strategist (Caesar aided the Blackfoot, a tribe, taught them how to use guns and military strategies, thus won the war against other tribes).
9. Terrorize attacks using Hit & Run tactic (Ranger Station Charlie, Camp Searchlight, Nelson, Nipton).
10. Absolute disciplined soldiers, obey without questions - thus make them more effective.
11. Higher level of safety guaranteed for traders (no/little raiders in their territory).
12. High ranking troops (Centurions) use more advanced weapons than even the lots of NCR (Anti-material rifles in game, carbines).
- Not sure if the Legion could fix the howitzer at their camp without the Courier's help, however, they do know that the Boomers have parts to fix them, so I'm not sure whether they can get it and fix the howitzer and uses it in the 2nd war or not so this won't count as one.
13. Spies in NCR's forces.
14. Dogs. It's all about the dogs. I mean mongrels.