Here's a comparison chart from Electronic Design:
And here's another from Benzo Energy:
These may not be all inclusive, but whether you can replace one with the other depends on which of the attributes are being utilized. For a phone, the non-cylindrical form factor and lack of liquid electrolyte are relatively irreplacable advantages. In addition to this for a device frequently held close to the body and unmonitored, the cells inflate their plastic bag in most failure modes and push the back off the phone, making it clear that maintenance is necessary, typically without a fire.
Generally, you shouldn't use a lithium ion battery without protection, and ones sold without protection are for use in packs with overall protection or devices that provide protection separately. You can also greatly extend their lifespan by not using their full charge range.
It's also worth noting that you cannot replace chemistry or with a smaller cell without evaluating the charging and protection circuits. Switching to a larger cell may also be a risk of overcharging because cut off current is based on capacity, so you have to evaluate the charger circuit in that case as well. Thanks Russel McMahon for the correction.