As usual there are several issues. In my opinion, the correct answer depends on the question you ask.
The first issue is sink rate. Water is 700 times as dense as air. Therefore sink rate is not determined only by mass density (specific gravity), that is how heavy an object is relative to how much volume it displaces. Objects of higher specific gravity of the same shape will sink faster.
Here are the specific gravities of some metals.
The second issue is shape which determines drag. A fly that is fuzzy will sink slower than a fly that is streamlined when they are of equal mass density. That is why Czech nymphs are streamlined and slim. The generally do not have beads but they are slim and heavy for their size, so they sink quickly. They have less drag, and drag is important wince water is 700 times as dense a air.
Once a fly gets down, another factor takes over and that is the behavior of this heavy fly and compared to the drift of a natural. A fly that is much heavier than the natural nymph CANNOT drift like a natural nymph.
Take a look at this video at 1 min 10 seconds. There is a drifting stone fly nymph and imagine a heavy bead headed stone fly pattern. It cannot possibly act like the natural.
"The nymph is a weak swimmer and when subjected to the current. it become a weightless and utterly helpless creature."
There are several concepts that determine the likely hood of catching a fish with nymphs and what bead heads flies can and cannot do.
First, the fly has to be at the level of the fish to catch them. This means within 1 foot of the river bottom (the feeding level of the fish).
The next two important concepts are Effective Drift Length (EDL) and Natural Drift (ND).
When fishing with or without a strike indicator, for any given cast, the fastest sinking fly will get to the bottom fastest and therefore will have the longest EDL at the level of the feeding fish for any given cast.
However, a bead head fly does not drift like a natural nymph which is neutrally buoyant and weightless
(see video). An unweighted nymph actually drifts more naturally (ND).
So a bead head drops like a rock but also drifts like a rock.
I prefer to use unweighted nymphs and add weight to the leader/tippet. When fishing water of varying depth and speed, one should change weighted flies. Few fly fishers actually do this when fishing weighted flies. If they do add more weight, they will add split shot to the leader system.
If I have to adjust by adding split shot for various water types, it is easer to use unweighted flies which will drift more naturally and change the amount of lead I use. It is easier to add or remove lead than to change flies. You get a system that presents a more naturally drifting fly with a EDL equal to a bead head nymph.
Bead head nymphs do catch fish BUT they do so in rougher water where the naturals gets tossed about and the bouncing of the bead head on the bottom is difficult to tell from the natural. In my experience, bead heads perform poorly in slower waters. In these waters the bead head should be lead down stream as in euronymphing.
When the nymphs are suspended by a strike indicator, the level of fly and the speed of the fly is a function of the level set by the strike indicator and the speed of the strike indicator. The fly position and drift lane is controlled by the strike indicator. In this case the bead head and non weighted nymph fished with split shot function very similarly.