If it's only about location and rotation around the Z axis, it should be as simple as:
- Select the object you wanna align
- Go to Editmode Tab
- Select all A
- Make sure you are in Vertex Select mode CtrlTab
- Hold Shift and click a vertex twice, which you wanna use to align location
(makes it the active vertex)
- Enable Snapping ShiftTab
- Make it snap to vertices CtrlShiftTab
- Set Snap Target to Active
- Grab your object G and snap it to the other model's corresponding vetex
- Snap Cursor to Active ShiftS
- Change Pivot Point to 3D Cursor .
- Hold Shift and click a vertex twice, which you wanna use to lineup rotation
(make it active)
- Rotate the model R, constrain to Z axis and snap your vertex to the corresponding vertex of the other model
(this can be really tricky, try to make the models a bit transparent to see what you are snapping to)
Not sure if the vertex in step 12 needs to have the same Z location as the first vertex... But even then, it should be possible to use any vertex with a bit more effort, to be able to constrain the right rotation axis in step 13 - using a custom transform orientation, which you would have to set up first...
If the models did not align originally, you might be able to snap to edge instead in step 13...