An SSD will last longer physically, just by right of it not having any moving parts. They do wear out through use, but modern SSD's will last long past the point of their obsolescence so thats not a concern.
If you want to record surveillance footage, a HDD is a much better option. For instance a 3TB drive can be had for ~$150, while to get that much capacity with SSD's (you would need multiple unless you use PCI storage devices) would be more like $1500. Also there would be little benefit to to using an SSD anyway, the extra speed wouldn't help in this usage.
Either will be fine for 24/7 usage.
Same reasons as the above, better off with a HDD.