Tantalum caps fail short and explode only when current is applied. So they will never explode in storage.

Electrolytic caps fail open, and can bulge and explode due to gas buildup resulting from the decomposition of the electrolyte. That can happen in storage, although generally the degredation is much faster when powered.

Seen from storage safety point of view, tantalum caps are safer than electrolytic caps. Putting any hardware in storage without antistatic precautions is unwise, ESD doesn't affect caps, but can damage chips - sometimes invisibly, only failing much later. So if you want that hardware to keep working, alway observe ESD precautions.

Do you store any sugar in the house? https://www.csb.gov/imperial-sugar-company-du … osion-and-fire/

Yes, 30 year old mechanically tired Tantalums have a tendency of exploding when powered.
10 year old electrolytic caps have a tendency of drying and not working at all.
Brand new MLCC capacitors love nothing more than catch FIRE when mechanically stressed
https://www.youtube.com/watch?v=VwdnGbI5ls8
https://www.youtube.com/watch?v=QgKY5QWehME

Tantalums will age with time (but mostly by being in actual use) and one of their more spectacular failure modes is shorting out. This will lead to some „venting with flames“. However they will never ever break while not in use.

Electrolytics however might start leaking electrolyte onto the PCB even when not in use. However this is unlikely for certain makes and models. So in some sense electrolytics are more dangerous to hardware in storage.