All batteries (in contrast with capacitors) exhibit what is called variable charge efficiency. That is, when the voltage is low, forcing 1 coulomb of charge into the battery will allow you to deliver (almost) 1 coulomb of charge when discharging at that voltage. This is a charge efficiency of about 1. When a battery is nearing full charge, the charge efficiency will drop, often to quite low values. Since power is voltage times current, the "unused" current and power near full charge will show up as excess heat, and the battery will start to warm up. So power is not a useful measure of charge effectiveness.
In most chemistries, there exists a maximum voltage, above which all input power is wasted, and this condition usually will damage the battery, as well. In "standard" lead-acid cells, the electrolyte may actually start boiling.
In lithium cells, trying to charge above a certain voltage (nominally 4.2 volts for a 3.7 volt cell), the cell will be irreversibly damaged, and may catch fire.
In addition, your statement that
won't the battery be filled with weaker electrons? I mean this time
the battery will be filled with less-energy electrons than the
shows a really major misunderstanding of how batteries work, to the point that I'm not sure how to respond.
For instance, if you have 3.7 volt lithium cell and you try to charge it with "1 amps and 10 volt", a charger which will supply 10 volts and a maximum of 1 amp will current-limit at 1 amp, and the battery will show a voltage much less than 10 volts (and if it shows more than 4.2, you're hosed). Likewise, a "2 amps and 5 volt" will limit at 2 amps, and less then 4.2 volts - unless you're hosed. Now, it's true that, as a rule of thumb, the 2 amp charge will produce a full charge in (more or less) half the time as a 1 amp unit, but that's not at all what you're asking.
In all cases, the useful effect of charging is to change the composition of one or more molecules. In the case of lithium ions, the most common reaction is of the net form$$LiC_6 +CoC_2 \Leftarrow\Rightarrow C_6 +LiCoC_2 $$ and the reactions use the same electron energy regardless of the input current.