All engines are not alike when it comes to the effects of ingesting ash, anymore then saying that all volcanic ash is alike.
The variance is due to the various melting points of the particles of ash (vary with the volcano) and the operating temperatures of the engine when they ingest the ash. This is in regard to the largest risk which is the loss of power at altitude. Wear out modes due to errosion and blocking cooling holes take place over multiple flights and can be addressed by overhaul.
The gas turbine engine risk being dependent on its operating temperatures (in cruise) has been steadily going up as the engine designs get more efficient by running hotter.
To my knowledge there has never been a ash cause multiple engine loss of power for the likes of a B727, DC9, DC8, B707 etc. (perhaps explaining why some engines seem immune)
Disclaimer: The comments above are not meant to conflict with published procedures and are only general in nature for the benefit of casual questions.