I want to create a cube with partitions on current (1 day) and history (1 month) data. The current day partition needs to be updated intraday by data push. For performance, should I use one fact table with filters on the two partitions or use two separate fact tables? Thanks!

It doesn't make any difference in terms of run-time performance if you build MOLAP. regarding processing time
you need to build index on the filter column if you choose to use one fact table, otherwise, the processing time may suffer.