Is one big via better than multiple small vias when changing power traces and ground between layers?

Remember that the connection is made by the plating of the inside of the holes, so that on a board with two mils of plating in the vias, the current must flow through a tube with a two-mil wall thickness on the inside of your hole, possibly to a one-mil trace that touches only on the edge of the tube (if the hole was cleanly drilled, but that is a whole different topic). In your example, the nine 10-mil vias would have more copper cross section through the board than the one 50-mil via (roughly 9:5). This is important both for resistance at high currents and for skin effect at high frequencies.

The other consideration is cracking, especially when connecting to internal layers. Copper expands at a different rate than FR4 or other board material, so there will be more differential movement, and more stress, as the geometry gets larger if the board is cycled at temperature. Similarly, when the board is flexed during vibration or handling, a larger geometry means that the stress is greater on the joint between the hole plating and the trace.

For external layers only or two sided boards, I have seen single large vias with a piece of bus wire through and soldered on both sides for high power, but multiple small vias are usually better if you are dependent on the plating to carry the current.

Many small vias are better. Consider this configuration:



The measured inductance, as given in the source, is (nH) 0.61, 1.32, 2.00, 7.11, 15.7, and 10.3 for configuration A, B, C, D, E, and F respectively.

The reason for that is that via inductance increases slightly when the diameter is decreased. This is more than compensated for by having multiple vias in parallel. There are many approximations for the via inductance you can use to validate the above result, such as

$$L = 5.08 h \left( \ln \frac{4h}{d} + 1 \right) 10^{-9}.$$