When you approach a 3-4 stone how do you determine whether to kakari on the third or fourth line?

I for the most part always go to the fourth line as I am more familiar with those joseki.

Is there any principle that can help you dictate how to kakari the 3-4 stone?

Balance. You don't want all your stones (or your oppoenents) on the same line. But you need to learn a few simple low approach joseki so that you can evaluate which may be better in any situation.

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Still officially AGA 5d but I play so irregularly these days that I am probably only 3d or 4d over the board (but hopefully still 5d in terms of knowledge, theory and the ability to contribute).

Of course, 4th line can lead to more influence, 3rd more for territory.

But also, there are a lot more joseki for 3rd line 3-4 approach, so it can be more complicated. High can be complicated, too, but has fewer known joseki variations, so in some cases is easier.

I think 4th line is more popular in modern pro games, maybe for both of these reasons.

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be immersed

In general, though there are joseki that go the other way, the 4th line puts a little more emphasis on the side that the 3-4 stone was originally pointing and on center influence, while the third line puts more emphasis on the corner and the originally weak side of the 3-4 stone. The 4th line approach is also somewhat lighter than the 3rd line, so when the opponent outnumbers you, a 4th line approach (or a distant approach) may be more prudent.

In a sense, which way you approach can also depend on whether you want to treat the original 3-4 as a third line stone, and cap it, or as a 4th line stone, and aim to undermine it.

EDIT:
One other thing to consider is that if your opponent tenukis, would you rather have a 5-3 joseki or a 5-4 one to continue with? Both have their virtues, of course, and the applicability of this depends on how advisable tenuki is. If there's miai, as with another unapproached 3-4 stone, it seems quite possible, if it's the last unplayed corner, maybe not so much, depending on the rest of the board.