It should be stated that no mountain above 7k is easy and requires proper preparation and experience with altitude. Both Lenin peak and Muztagh Ata are popular and have a reputation of being easy mountains. Having been to both peaks let me share my experience.
Muztagh Ata normal route is easy from a technical point, not many steep sections, few crevasses. Base camp is easily reachable from Karakoram Highway by a 4×4 if need be. The main challenge is in the altitude, weather and distance. Camps are located far from one another resulting in long, tiring hikes between those. The summit is over 7500 m so the air is very thin, can be a problem with no oxygen for some climbers – after all it is 43rd peak in the world. As this volcano stands at the edge of mountain range the weather can change suddenly and is hard to predict resulting in low success rate for climbers. Usual 3-4 week give little time to wait for favourable conditions.
Lenin peak is cheaper option and requires fewer red tape being located in Kyrgyzstan and not in China. The camps are not as far apart, maybe except C1 – C2 route across the glacier. It is however more technically demanding. Glacier is quite dangerous with huge crevasses and many small ones that can be hidden. Summit ridge is often without snow – just stones and ice. One has to be more skilled climber, know how to walk with crampons on different terrain, also steeper slopes.
Overall both of these peaks represent similar level of difficulty, although for different reasons. For me having experience in ice and mixed climbing Lenin peak was easier. For people who only did easy routes like Mont Blanc and Elbrus before and are not alpine climbers I would suggest Muztagh Ata.