You had better have a good reason to go to Leadville in March like snow shoeing or skiing. It is one of their heaviest snow months. I think the only place you will have to camp is downtown. All the BLM/Forest Service campgrounds will still me under feet of snow. You might think about staying in Buena Vista. It is almost 2,000 feet lower than Leadville. It is about a 45 minute commute.
Either of your route are ok. I prefer the Freemont Pass route as opposed to Tennessee Pass. Road grade is more gradual and is in better condition.