Federal's softer cup primer has LONG been the go-to choice for competitive revolver shooters for whom a light hammer strike must reliably detonate their cartridge. A light hammer strike is one product of a lighter hammer spring (which gives a lighter double-action trigger pull) so having a soft-cup primer is certainly the best way to (hope to?) maintain reliable ignition while lightening hammer spring tension.
One of the side effects of an easier to detonate primer has been detailed well already -- they don't stand up to heavier loads.
But the other thing to consider and keep watch for is the liability of unintentionally detonating one at the bench while priming.
Lee has carried warnings in their priming tools and progressive presses for many, many years, going back to the 80's IIRC about using only Winchester or CCI primers in their equipment, to guard against unintentional detonation.
I don't see why Lee equipment is any "rougher" when it comes to priming cases than other brands or colors of equipment, but they have continued their use of that particular warning. They never spelled out Federal as a specific problem, but they did (and still do?) say that Winchester and CCI were less susceptible to the issue.
Attention Brass rats and other reloaders: I really need .327 Federal Magnum brass, no lot size too small. Tell me what caliber you need and I'll see what I have to swap. PM me and we'll discuss.