Another great question. First lets go over exactly what each type of deadbolt is and then we can get in to why you would use one over the other.
This style of deadbolt is definitely more commonly used on exterior doors. It's simply a keyed cylinder to lock/unlock the door with a key from the outside and will have a thumb turn on the inside.
A double cylinder deadbolt has a keyed cylinder to unlock the door with a key on the outside (just like the single cylinder) as well as on the inside. Yes, that means that you will need a key to unlock and lock the door from the inside.
A double cylinder deadbolt is great for the doors that have partial glass. The reason being in case there was an intruder and they wanted to break the glass so they could unlock the deadbolt from the inside and enter, they won't be able to because it would require a key to enter.
The more obvious choice may seem to be the double cylinder because it's got two keyed cylinders and is more secure right? It really is a great deadbolt to have, but be aware that a double cylinder could possibly be a fire hazard because you or any other member of your family would require a key to get out. You may have to pick your battle with this style. Either you feel more secure with a double cylinder because you have partial glass, or you feel more secure without double cylinder because it may be a fire hazard. When customers ask us which is better, a single cylinder or a double cylinder, we mention the fire hazard thing so they are aware that it could be dangerous if you need to exit, but that it really does bring ease to others because of its security. Like I said, you have to pick your battle.