I've done it both ways and like the others said it depends upon door height, etc. I done both in the same trailer. A soft soggy particle board floor as you suggest may also have water damage to the insulation underneath so you may want to remove it. Remember the floor and covering was laid before putting up any walls so the flooring runs under walls and you may have damage in other rooms or hallways. You may be able to fix insulation from underneath. If the damage isn't too bad in an entire room then overlay it if you want. Use 3/4" cdx plywood or osb except the new stuff is undersized so you may need some roofing felt to get it even with the rest if you are replacing it.
You can also get water damage from leaks around windows and doors running down the inside of the siding and never know it under the floor covering. It can also leak down the inside of the siding from the roof line. Use a circular saw to cut out old flooring and hammer and chisel the rest under walls. Have fun.