Both S5 Mini and S6 Mini are ought to be the smaller replication of their bigger counterparts.
Since we would never like to guide you wrong by providing false information, so we are mentioning only those differences which we are pretty much sure of.
|Subject||S5 Mini||S6 Mini|
|Camera||10 MP||12 MP with 4K capabilities|
|RAM||2 GB||2GB to 4GB (expected)|
|Android||4.2.2 Jellybean (same as that of S4 Mini)||Android 5.0 Key Lime Pie (same as that of S6)|
However for detailed study about S6 you may see S6 specifications.
* Subject to change..!!