Compare data with variable period

Mate, I can see you've got a data modeling problem, not a DAX problem :)

Here's how I see it. Let's say each week you get a new snapshot of the same shape, only measurements change. Snapshots are S_i, i=1,...,n. Each snapshot has columns C_j, j=1,...,m. One of the columns, but fixed, in each of the snapshots must identify the snapshot, say its name's SnapshotID (or SnapshotName, whatever that makes the snapshot rows unique among all the rows from all the snapshots). Then you stack up the snapshots on top each other. This is the Master Snapshot (your fact table). Then out of this you create your dimensions using PQ (if you have not yet done it), or the so-called lookup tables, and you join them to the right columns in the Master Snapshot (which should be hidden as much as the other snapshots, if you've imported them into your model). 

This way you've created the celebrated STAR SCHEMA :) Once you've got this, the rest is rather easy. One of the dimensions (lookup tables) should hold the identifiers of the individual snapshots (SnapshotName or SnapshotID), so that you can create a slicer and select the snapshot you want to compare to. If the latest snapshot is the one you always want to compare the others to, then you could call it something like "Most Recent" as the SnapshotName (or SnapshotID). You could also store the latest snapshot separately from the old ones (which you've combined into the Master Snapshot). Both, the latest and the MS would be hidden anyway because in a good model only the dimensions are exposed together with measures. Bear in mind that dimensions should join to facts in a 1:many fashion.

Once you've done the data modeling part, you can write your measures. Let's say that you have the Master Snapshot with historical data and the Most Recent snapshot separated. You would then create a slicer that would hold the identifiers of the old snapshots (the ones to compare with the most recent one). For each metric you'd want to make a comparison with you'd define 2 measures - one measure would calculate the thing on the MS and the other on the Most Recent.

Put the slicer with the names of the historical snapshots on the canvass. Let the user select only one identifier at a time. Then create a table/matrix to show values from the MS (which will be filtered by the slicer) and the same metric defined for the Most Recent snapshot (which will act independently of the selection in the slicer).

You could also, alternatively, put all the snapshots into one Master Snapshot, together with the latest one, and basically do the same as above. The only change you'd need is adjusting the measures so that there is one that always shows data from the Most Recent snapshot and the other one from the one you've selected in the slicer. But that's a cinch.

Best

Darek