Data is inserted into a columnstore index during the index build process in the order of the underlying clustered B-tree index, if there is one. So method 1 is preferred to give the best segment elimination.
Even if the underlying data in the table is a heap, if you partition the table by Date (method 2), every segment within a partition has dates greater than all preceding partitions and less than all following partitions. For example, if you partition by day, and there are five million rows per day, then there will be five columnstore segments per day. If the underlying table does not have a B-tree index on date, then data for these five segments will not be sorted by Date. But the table will be approximately ordered by Date simply due to the partitioning. This approximate order will be enough so that you'll get very good partition elimination for filters on Date. The following table illustrates this for two days worth of data.