they are cheap but here's something to consider. if you do get a puncture, and you have the repair kit with you ( i'm assuming here you have a slow leak that you notice and not some sort of blow out, emergency situation), it works by reaming out the hole with the provided rasp/file. then inserting the plug (possibly with included glue/sealer). the problem is during this process you're losing more air. so even if you get the hole plugged, you now need to blow up the tire, so unless you're also carrying a tire inflator, you're really not going to be able to go anywhere.
Patching is a much better scenario just like a car, but of course you need to do that at a shop or similar location that has the required machines ; ie-a rim clamp, and tire balancer, since it requires removing tire from rim. this is a much more permanent repair, but again you'd need a tow or whatever to move the bike
i think in my own experience if i had a puncture, regardless if i could make it to where i was going or not, i would spend the money and replace the tire rather than risk the repair not holding 100%. i mean my life is much more at risk on 2 wheels, and if 1 of them has a leak.. those aren't good odds to me, so i'd just start over rather than repairing the old one.
just my 2 cents.