This reminds me of cancer diagnostics, where old gene expression signatures are replaced by newer ones, that are of course supposed to be better. But how to show that they are better?
Here are a couple of suggestions to compare the repeatability of the methods.
1. Use co-inertia analysis (CIA).
CIA should be more advertised, unfortunately it is not widely used (no Wikipedia page for example). CIA is a two-table method that works on the same principle as canonical analysis (CA), which is to look for a pair of linear scores with maximum correlation between two sets of multi-densional measurements. Its advantage over CA is that you can do it even if you have more dimensions than observations. You could measure both methods on the same samples to get two coupled tables of 30 columns and $n$ observations. The first pair of principal components should be strongly correlated (if methods really measure the same thing). If method B is better, the residual variance should be smaller than the residual variance of method A. With this approach you address both the agreement of the methods, and their disagreement, which you interpret as noise.
2. Use a distance.
You could use the Euclidean distance in 30 dimensions between the test and the retest to measure the repeatability of a method. You generate a sample of that score for each method and you can compare the samples with the Wilcoxon test.
3. Use downstream application.
You are probably getting these fingerprints to take a decision, or classify patients or biological material. You can count the agreements vs disagreements between tests and retests for both methods and compare them with the Wilcoxon test.
Method 3 is the simplest, but also the most down to earth. Even for high dimensional inputs, decisions are usually quite simple. And however complex our problem is, bear in mind that statistics is the science of decision.
Regarding the question in your comment.
What about using a robust dimensionality reduction method to reduce the multivariate data to a single dimension and analyzing it?
Dimensionality reduction, however robust, will be associated with a loss of variance. If there is a way to transform your multivariate fingerprint into a single score capturing almost all of its variance, then sure, this is by far the best thing to do. But then why is the fingerprint multivariate in the first place?
I assumed from the context of the OP that the fingerprint is multivariate precisely because it is hard to reduce its dimensionality further without losing information. In that case, their repeatability on a single score does not have to be a good proxy for the overall repeatability, because you may neglect the majority of the variance (close to 29/30 in the worst case).