From what I know, perf boards have individual copper holes but stripboards have rows of connected copper. Are there any difference besides their appearance? ie such as the limitations of voltage or current they can handle?
Two aspects come to my mind for selecting between perf and strip board for prototyping.
The strip board comes with a pre-fabricated connectivity between all the points on one strip. As this will surely not match your intended circuitry, you have to cut some strips, as well as add some wire connections.
The (copper-plated) perf board comes with all points isolated, so you have to do all connections by adding wire.
Only you can decide which starting point you prefer.
On typical perf boards, the copper pads tend to come loose with excess heat. This isn't such an issue with strip boards, as there's more adhesive area available under the copper strip. So, with a perf board, no need to be more careful while soldering.
There are as well perf boards without copper pads with the disadvantage that you can't keep your components in place by soldering. They may be useful if you prefer wire-wrap connections.
Voltage and Current
As long as you keep within the typical low-power electronics applications (voltages below 24V, currents below 1A), both board types will be okay.
Anyway, stay away from higher voltages unless you know what you're doing.
Let me add some consideration at the good answer already give to this question. This consideration are based on my personal experience.
frequency keep in mind that capacitance between traces can give problems so they are not suitable for radio frequency constructions.
debug with strip boards is common to have short circuits due to little droplets of tin mixed with flux that sits between traces. When you cut traces keep the chips away to not have shorts. Clean the board after soldering.
number and density of components use plenty of space between component, they are designed for prototype in fact it's easy to change, cut, piggyback solder on those boards. Even if you are making your final versione of the board use plenty of space between them.