Everest Base Camp Tibet
Having done both sides now, I can say that Everest on the North Side is a WILDLY different experience. It is medically easier and safer, but it's more expensive and has its own dangers. Let me go through the process.
(1) The visas. So assuming you are not a Chinese citizen, or the citizen of certain South Asian countries who can get permissions more easily, there's a multiple-step visa process to enter Tibet. First you have to get a Chinese multi-entry permit visa, and with this one you have to present a plane ticket, an itinerary that shows where you'll be every day, and hotel confirmations. There's more to this process that I won't post directly but you can PM me about it
(2) Once you have the Chinese visa, you book a tour through one of the official government-approved companies that provides Westerners with tours to Tibet. You want an ethnically-Tibetan-run one, because going with a Chinese one will give you ... a very different experience. You show them your Chinese visa and they then can apply for your Tibet visa, as well as the permit to enter the Everest nature reserve zone. You have to hire an official guide to handle the paperwork and get you through the checkpoints, register you at the different hotels and police departments, and handle anything else that comes up. The visa takes about a month, but sometimes the Chinese government withholds it until a few days before your departure. For funsies. Also, March is completely off-limits because of "sensitive" anniversaries.
(3) You fly to Beijing (or another point of entry) and receive your Tibetan visa, which you can't receive until you're in China. Then you can fly or take the train to Tibet. The train takes 2 days. You can fly directly to Lhasa (which I did) but some people fly from Beijing to Chengdu, stay overnight in Chengdu, and then fly to Lhasa because of the altitude jump.
(4) Lhasa, the capital of Tibet, is about the height of Namche Bazaar. That means you have to be there a few days and spend the first bit of it resting. Like, don't even go for a serious walk the first day because I did that because I was so excited to be in Tibet and the next day I dealt with poor sleep and a bad headache. I did not wake up breathless like on the trek, but I did get winded from basically any steps. They sell oxygen by the bottle in Lhasa and all over Tibet and there's oxygen in the hotel rooms, but it's better NOT to use it because you need to adjust and it will slow that down. I was in Lhasa for 4 nights. There's a lot to do in Lhasa.
(5) Lhasa to Shigatse. Shigatse is a higher own. The Tashilumpo Monastery is there, though not much else. Most people stay overnight and do the monastery and then move on.
(6) Shigatse to EBC. About an 8 hour drive. Checkpoints, not a lot out there, but beautiful landscapes. Also I hope you like meat, because if you ask for vegetarian food you will get a plate of fried rice like I did. EBC itself is the tourist EBC, which has hotels, lookout points, and Rongbuk Monastery. The climber EBC is elsewhere. You have to board a special bus to drive there. A lot of people around you will be using oxygen at this point, including some people on oxygen through a nose tube. Some people bring their kids and use that for their kids. Though this was the highest I'd be going (obviously), as I was going to continue along the high plateau to Darchen to see Mount Kailash, I didn't use oxygen. I didn't use oxygen the whole trip, and suffered from mild headaches and trouble sleeping, but felt much better as I descended on the way back.
(7) EBC. Unlike in Nepal, Everest is SUPER visible, as you can see. The general itinerary is arrive in the afternoon, see sunset, go to sleep (you WILL be tired), then see sunrise, then Rongbuk monastery, then leave. There's not a lot else to do there. They have oxygen pods where people can sit in and look at the mountain, the hotel rooms have oxygen, and they're building a restaurant that overlooks Everest that isn't finished yet. There's no real trekking here, except from the monastery to the best lookout point, and that's 10 minutes. Chinese tourists come with their families. Oxygen bottles - the ones you just huff like in Spaceballs - cost 10 yuan, which is about $1.50. Maybe more depending on where you buy it.
It is POSSIBLE to go to EBC from Kathmandu, but it depends what's going on politically and what passes are open. It's not super nearby - most people leave from Kathmandu to go to Mount Kailash, a Hindu-Buddhist-Jain pilgrimage site the birthplace of Shiva. That's about a 20-day roundtrip, which includes a kora (circambulation) around the mountain, which takes 3 days and people occasionally die on because of altitude problems. Like a few a year, and it's usually elderly pilgrims whose tour companies skimped on the oxygen.
It was an incredible trip. It is a different thing to have a full view of Everest that you can just stare at for as long as you want. I also like the view much better. I'm so glad I did it.