We need to replicate one of our enterprise SQL Server database to DR site for HA purpose, due to budget reason, we would like to install another SQL Server Express rather than the enterprise or standard version. I think that both Transactional Replication or Merge Replication would work for this case, which one should work better for this situation?
Have a look at this article by Brent Ozar.
The main idea is that you can have a replica, which you do not have to pay for, as long as you do not query it.
Details are in the article.