It's very much hit or miss, if one is using car speakers on a boombox.
Personally I would seek speakers that have:
Numbers:
Low RMS power rating (5-30W)
High SPL
Low Fs (low resonant frequency, 30-60Hz max) (or rated frequency response going as low as possible)
Low Mms (moving mass)
High X-max
High Qts
Look & feel
Very loose suspension (soft upper surround and "loose" cone)
Small/smallish magnet (probably smaller and lighter voice coil too - higher sensitivity) often small magnets are also made from better material, so they can be more powerful in comparison to big sized/weak magnets.
Forget:
Max power
Big magnet size
The original speakers are mostly 3.2 or 4 ohms, but I've never seen any detailed data of them, but I bet they have high sensitivity (SPL) too. Also the original speakers have tiny voice coils, minimal moving mass and low RMS power. The maximum power of a boombox is usually something from 2W to 15W per channel. And that's the power at 10% THD, or total harmonic distortion. Remember, distortion heats up the amp and the voice coil and in long run, will do at least some damage.
There is really not much point of using high power speakers. Those are designed to be run with higher power and possibly wont be the ideal choice. Of course some higher quality products can make a good replacement.
I would personally search for some OEM car speakers, for example speakers that are used in more high-end cars. I've seen 2ohm speakers too, that probably would be heavy hitting things in some boxes with proper amp&cooling. Those OEM speakers often have light weight cones, soft foam surrounds and RMS power rating of 10-30W. Some of them (rare) also feature a low impedance voice coils.