The Virunga Mountains at the borders of Rwanda, Uganda and Democratic Republic of Congo are home to around 480 mountain gorillas, more than half of the world’s entire population. The rest live in Bwindi Impenetrable Forest in Uganda. In Volcanoes National Park, the Rwandan part of Virungas, ten gorilla groups are now habituated for gorillas safaris, more than anywhere in the world.
Gorilla trekking safaris can be done throughout the year. The hiking itself can be more difficult in the rainy season from April-May and in November, but at an altitude of 2000m and more, it can of course rain here at any time of the year. The most popular times for gorilla trekking are during the drier months, between December and February and from about June to mid-September.
Gorilla permits in Rwanda have recently (as of 2012) increased to $750 per person. They are $500 per person in Uganda. The permit gets you an hour of time spent with the gorillas with an 8 person group. If you buck at the price think of it this way. You are contributing to the preservation of gorillas and as a “thank you” you get to spend an hour with them. Remember only 56 people a day get to see them and their habitat is very fragile. Every time you walk through the forest you are leaving a footprint.
Rwanda provides the easiest access to gorilla trekking so it is your best option if you are combining it with a safari to Kenya or Tanzania or if you only have a few days. The town of Ruhengeri, the jumping off point for trekking in Volcanoes National Park, is only a few hours drive on excellent roads from the capital (and its international airport) Kigali. Seeing gorillas in Uganda is more of a process and involves an 8-10 hour drive from the international airport in Entebbe. I recommend making Uganda a full 8-day trip with stops along the way instead of just a place to see gorillas whereas you could see gorillas in Rwanda in just a few days.
Seeing mountain gorillas can involve 2-4 hours of hiking to find them. In both Uganda and Rwanda this is going to be a long day and the hikes can vary quite a bit depending on where the animals spent the night and which troop you are seeing. That being said, the general experience is that treks in Rwanda are slightly easier while those in Uganda are slightly more strenuous. And there are no guarantees either way.
There is no difference. There are 10 habituated troops in Rwanda and 8 in Uganda and they can move freely between the countries so this really doesn’t need to be a consideration. The gorilla trekking system is similar in all countries and because gorillas are followed on a daily basis, a sighting in all the locations is virtually guaranteed.