How to choose the correct transistor?
You are (presumably) comparing a MOSFET with a BJT.
When you are using the transistor as a simple switch, the control current is what matters in the latter, and the voltage in the former.
In the case of the ancient 2N3055, you need to put 400mA into the base in order to have Vce drop to 1.1V (max) at 4A.
BJTs are different from MOSFETs are different from IGBTs and so on, so you need to get a basic understanding of how these parts work in order to interpret the datasheets.
For example, a MOSFET such as the PSMNR60-25YLH you can see that 4.5V or 10V will turn on the transistor to varying degrees with 25A drain current flowing. At 4A the 3055 will dissipate almost 5W, whereas the MOSFET linked above will dissipate 11mW with 10V drive or 16mW with 4.5V drive. That several hundred to one reduction in wasted heat/energy is why bipolar transistors are not very  popular in modern times for switching low voltages at relatively high currents.
BJTs do not really have an Rds(on) like MOSFETs. The voltage drop is not linearly dependent on current as MOSFETs are (at least until Vds starts to approach Vgs(th)). So you find Rds(on) but not Rce(on) (Zetex marketing aside).

Edit: Here is the approximate circuit and a simulation:



simulate this circuit &ndash; Schematic created using CircuitLab