I have done the three treks that you mentioned and many others. EBC, Annapurna Circuit, and the trek to Gokyo are all fantastic. You won't go wrong on any of these. What are you looking for in a trek and how much time do you have and what time of year are you trekking? I think the Annapurna Circuit has the edge on a cultural experience because you are traveling through so many different villages at different elevations. Roads have been built in this area, even along the trek, but it most places, its easy to get off the road and hike on a trail on the other side of the valley. Some posters will say this trek has been ruined by the road building. I think it still has a lot to offer. The Annapurna Circuit also has good mountain views, but not as many "in your face" mountain views as compared with the Everest and Gokyo areas. Of course, if you have the time, you can easily do Everest Base Camp and the Gokyo valley in one trek. Most trekkers never actually go to Everest Base Camp. Most trek to Gorak Shep, and climb Kala Pattar for great views of Everest. You can not see the top of Everest from Everest Base Camp. The base camp itself is rock and ice and very disappointing to most people. However, the entire trek to Gorak Shep is simply stunning with all the high mountain peaks. If you trek to Gokyo, certainly climb Gokyo Ri. I recommend climbing this peak (on a good walking trail) in the late afternoon for incredible sunset views of Everest. Also, take the time to spend a long full day walking up to 5th and 6th lakes, above Gokyo. For more of a cultural experience, you could start your Everest/Gokyo trek at Jiri. Most people fly into Lukla to do this trek. Few trek in from Jiri. Its a wonderful trek with few tourists. I highly recommend it, especially if you are looking for more of a cultural experience.
All these treks are scenic. Busy is relative. It will depend on the time of year, but the Everest trek will seem the busiest. The trek from Jiri to Namche (Everest region) will be the least busy. The level of difficulty depends on what you've done and what you expect. If you've never trekked to 5000 m before, all three will probably seem difficult. However, the key is just to go slow and acclimate properly. I've met western trekkers in their 70's and early 80's do these treks so you can too. Above 3000 m, your sleeping elevation should not increase over 300 to 500 m per night. Sleeping elevation is important because you spend so much time doing it. The Gokyo valley is quite steep so you trekking days to acclimate will be quite short - maybe only 2 or 3 hours. It's very important to acclimate properly. The helicopter pilots call the Gokyo valley, the "valley of death" because so many people feel good and trek too high too fast and end up on their death bed in the middle of the night. Don't be one of these people. Acclimate sensibly. I have never known anyone to get altitude sick, if they are healthy (ie. no respiratory infection) if they follow the acclimatization guidelines that I mentioned above, especially if they follow the lower limit of 300 m per night.
Do you want to trek through snow and ice? All of these treks have the potential to do so.