Finally the Covenant are just like any other army, they have to deal with the logistics of moving larger numbers of soldiers from Point A to Point B. Do you think that when they invade a city they just instantly plop down a couple thousand soldiers? No because they wouldn't have enough Spirits, Phantoms, drop pods and other transports to do so. Rather they would deploy them in waves like a real army or as seen in Firefight. In fact that would be how they did in Reach's case regardless of the version. In The Fall of Reach they had the Covenant invade the planet from the poles but do you really think they just a ton of soldiers and had them march across the planet? No they would have deployed fleets of dropships and transports carrying the soldiers to their targets. And that's actually why I don't like how quick that first version of Reach's fall was. Now I have no doubt that the Covenant ground forces they deployed numbered in the millions but here's the problems with that, A) this is Reach, the center of the UNSC's military and had an appropriately massive military presence (later Bungie confirmed it's total military manpower to be over 385,000,000) and B) those millions of Covenant would have spread across an entire planet. Now on any other planet they would have overrun things quite quickly but again this was Reach. Yeah the Covenant would have won in the end but even they couldn't have crushed Reach that quickly. They would have ground down the UNSC at first, picking up momentum until there was no stopping them. You know like how they've described many of the battles for other worlds the Covenant have conquered.
But remember, they're entire armada attacked Reach. At the beginning, the troops swarming the poles was just the tip of the Iceberg. What do you think would have happened once the Super Mac Guns in orbit were taken out, and the entire covenent armada had their troops launching towards the surface? That is millions upon millions upon millions more troops going towards the surface. The covenent had the numbers and technology to overwhelm the planet in a day. That is believable to me. The main defences were the super mac guns. Once those went, everyone knew that Reach was done. That is why I liked the book. That was the true feeling of hopelessness. Once the guns were down, once the fleet was scattered, Reach was done for. Hell, the conflict on Reach was even expanded in First Strike. It gave a first hand look at the odds on Reach. Even the surviving spartans experience that feeling of hopelessness.
The book was more believable than the game, IMHO. Seemingly endless numbers of enemies being launched from orbit mixed with superior numbers, tactically sound commanders, and superior technology, would meet with the believable ending of Reach falling in a day. To me, there is no way they could have held out for months. Not with the entire covenent force arrayed against them.
The Covenent knew what to expect of Reach. They were ready to attack. Their other engagements on other planets were smaller fleets attacking, thus meaning smaller forces arrayed against the defenders, thus meaning more time taken to conquer said planets.
Earth is a different story though. They had more Super Mac guns, the remainder of their entire fleet was in orbit or en route to Earth, it was their last bastion of defence. Their homeworld. The defenders knew what they were fighting to defend. They knew the cost of losing. That meant they would fight harder than the Reach defenders were able to. The defenders at Earth were ready for the Covenent unlike at Reach.