Use parallel or series circuit for high power LED strip lights?
This entirely depends on what you call a "strip"... So make sure you know what you are ordering.

The most commonly available is the flexible LED strip. Here is an example. You can also get them on metal-core PCBs.



Important things to notice are "24V DC" labeling, and presence of resistors. As is usually the case, white LEDs having an approximate Vf of 3-3.3V are wired as series groups of 3 LEDs for a 12V strip, or 6 LEDs for a 24V strip. Each group has its own resistor to set the current, and all groups are then wired in parallel. The strip can be cut between each group of LEDs.

These trade some efficiency for convenience. Resistors do waste some power, but you can simply wire the strips in parallel and use a constant voltage power supply.

There's a subtlety though: if you connect two strips together using the terminals at the end to make a longer strip, they kind of look like they're wired "in series" ... but they are not, this is parallel wiring since both + and - of one strip are connected to + and - of the next strip.

Note that copper traces on these are usually quite thin, so if you use a long high-power strip, drawing several amps, you might want to supply it from both ends or from the middle instead of at just one end, as voltage drop due to copper resistance can cause a drop in luminosity the further away you get from the supply connector. Likewise wiring several strips one after the other may cause drops in brightness. You can measure the voltage along the strip to make sure it's uniform.

Now there also "strips" which contain just LEDs and no resistors like this one.



These also contain series-parallel groups of LEDs (or sometimes just one group) but no resistors. Presumably LEDs are binned by Vf to ensure adequate current sharing.

However, since these do not include resistors for higher efficieny, you must not use a constant voltage supply, rather use a constant current supply able to output the voltage that the LED module requires.

These can also be wired in parallel, but since there are no resistors, balanced current sharing is an issue.