Many people (especially on servers) argue about this. In this article, I will discuss the pros and cons of both. Now let me start off by saying that there is no true answer. A large part of it is how patient are you. Anyways here we go.

First let's talk about caving. For those of you who don't know what caving is, it is exploring cave systems (duh). There are several reasons to do this. The prime one being the fact that there is a lot of exposed ore. Even a small cave system could hold a stack or two of iron. Another reason to do this is for building a mob trap. Now, this previous reason only applies to single player and small servers. Basically when I say for a mob trap, i mean lighting up the entire underground, a feat that would be obviously impossible by strip mining. You would want to light up caves in order to prevent mob spawning there and encourage it in your trap. The reason you can't do this on most servers is that there is a cap to the number of hostile mobs. But, this cap is applied to all players. That means everyone on the server would have to light up their area to give your mob trap even decent efficiency. Now there are several cons to caving. The main one involves dying. Not only will there be mobs (something you will rarely encounter while strip mining), but also you will be prone to falling into stuff. When you dig out ore on the floor, there is a decent chance you could fall into another cave, a ravine, or worse, lava.

Now for strip mining. This is essentially making a small room and digging long 1x1x2 tunnels usually at level 12 (diamonds are most common at this level). Now, the main benefit to this being that it is the most resource efficient. You don't need to carry a sword or armor while you are mining. Plus, you don't need as much food as you wont be doing as much jumping (which consumes a lot of hunger). You will also go through much less torches do to the fact that you don't need to cover as much horizontal distance with light. A null point (good or bad depending on the situation) would be that you accumulate a lot of cobblestone. Lastly, (for the positive points) is that you are unlikely to fall into lava (assuming you are not digging out one block at a time) as you can usually here it and be prepared.
Now for the bad. You will consume pickaxes at a much faster rate (if you use stone pickaxes this is not necessarily bad as you will have tons of cobble). Another problem being that on a server, you will be likely to encounter another person with the same idea. (again could go either way as you know where there base is but they also now where your base is) The main problem with this is that it takes a rather long time to be very effective. So if you don't need a lot of stuff, or are not playing on a server/world you intend to be on for a while I would highly unrecommend this.

In conclusion it depends on the situation on which to use. "Is this a world I'm going to spend a lot of time on?"should be the main question. Also, it depends on how much you want. Let's say you want an iron sword. Then you would go caving as it should be rather easy to get 2 iron. But, let's say you are getting ready to fight the wither/enderdragon. Then you would want to strip mine as to get all the gear you will want, it will take half a stack of iron, which would be easy to find in that amount using 1-2 stone picks. So have fun mining whichever choice you make. I hoped this helped.