At least in the US, the argument is that when pressed by the FDA, Novamin was pulled from the market by GlaxoSmithKline instead of doing the required trials whereas Biomin went through and passed all the trials.
And since it's actually gone through the process, there are studies out that compare it to other hydroxyapatite solutions. I've linked one study which compares their two variants against Apacare and karex (two HAp toothepaste which have studies of their own that compare against the others before them like Novamin).
The study shows that Biomin C (the one without Fluoride) is comparable to karex (the one without fluoride) and other similar HAp toothepastes. HAp + fluoride (like novamin) marginally outperforms it. So if you use fluoride (such as by also using a fluoride toothpaste or living in an area with fluoride in the water) the difference should be negligible. Importantly though for people in the US, Biomin C is available here.
Biomin F is wrapping up the FDA approval process however it does seem to generally outperform all other formulations since the fluoride is actually part of the bioglass itself rather than simply an additional active ingredient in the suspension.
TLDR: Biomin C is within marginal differences to comparable no-fluoride HAp toothpastes on the market but Biomin F outperforms other HAp toothpastes that contain fluoride since the fluoride in Biomin F is delivered via the same mechanism that handles remineralisation of the other elements. And to my knowledge Biomin F is the only HAp toothpaste to do that so far. Also Biomin C is the only HAp toothpaste available in the US (with Biomin F apparently soon to follow).
