I‘ve heard that plugged tires are dangerous and that patched tires are safer. I‘m not talking about the sidewall but the tread.
When someone plugs a tire by definition they have not inspected the inside the tire for possible damage. Trust me, in 8 years in the tire industry I have seen hundreds of tires that looked just fine on the outside (excepting that pesky nail or screw hole) but when you dismount them you find a shredded inner line (the part of the tire that keeps the air in) and handfulls of powdered rubber that used to be part of the tire.
As others already said, plugs come out. Usually at the most inconvenient time too. Plugs are a good temporary fix, assuming you can also air the tire where you install it. But any tire plugged should as soon as possible, be taken to a good shop where the tire can be dismounted and the plug cut/ground off. Then, a patch should be placed over the spot.
Plugged tires are more dangerous because plugs can come out, resulting in a sudden loss of air pressure. A patch covers the hole from the inside of the tire and can't come out, so no danger of a sudden flat tire.