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But only if the LED strips have the LEDs in each type using the same current for the same brightness. I am guessing that the LEDs in the 4.5V strip are much dimmer and use much less current than the LEDs in the 12V strip then they will not work in your application.Alright, that makes sense So if I'm understanding correctly, 3 AA's would just run a 5V strip for (3/8) as long as 8 AAs would run a 12V strip.
I am guessing that a 4.5V LED strip will work a little brighter when powered from a 5V cell phone power bank. You need to try it to see if it is bright enough.In which case, just for convenience, since portable cell phone chargers are so much more plentiful than 12V battery packs, it seems 5V would be a better choice. Much easier & more cost-effective to find 5V battery packs than 12V, all else equal. Again, if I'm understanding correctly
You never told us the length of the LED strip needed (therefore the number of LEDs and the amount of battery current needed).