"Higher plants" or "vascular plants"?
Is one of the terms preferred over the other?


Absolutely: "vascular plants" is the preferred one. "Higher plants" should be avoided. Here is a long explanation:

The Great Chain of Being

This term "higher plants", together with the term "higher animals", is just a remnant of a completely wrong concept that has (or shouldn't have) no place in the world after 1859: the Great Chain of Being, or scala naturae  in Latin.

This is the typical medieval representation of the scala naturae:



The Latin text on the ladder says: stone, fire, plant, beast, man, heaven, angel, god.

And here a more "modern" version of it (but equally wrong):



Unfortunately, this absurdity survived until the late twentieth century, and can be seen even today in some books/sites/lectures.

Linnaean Taxonomy

To understand the use of "higher plants" (and "higher animals") in biology, we have to go back a little in time.

When Linnaeus published his Systema Naturae, he divided the nature (Imperium Naturae) in 3 Kingdoms:


Regnum Animale: the animals;
Regnum Vegetabile: the plants;
Regnum Lapideum: the minerals (you read it right).


Note that, in this classification, "animals" correspond to what nowadays we call animals and protozoans, and "plants" correspond to what nowadays we call plants, algae, fungi and bacteria.

You have to keep in mind that this book was first published in 1735, well before the evolutionary biology being proposed in the XIX century and established in the XX century. Therefore, it is a book published when fixism was the current paradigm, full of mentions to the scala naturae.

So, the plants (as well as the animals) showed a continuum of species, going to the lower plants (the bacteria) to the higher plants (the flowering ones). It's worth mentioning again that, by that time, bacteria were plants: Phylum Schyzophyta, to be more precise.

Thus, we have "lower plants" and "higher plants", "lower animals" and "higher animals", as well as "lower minerals" and "higher minerals"!

Unfortunately, this terminology is so embedded in the biological sciences that even today, as I mentioned, we struggle to get rid of it.

Just drop "higher plants", whatever it means

As your Wikipedia link says, "higher plants" is a synonym of vascular plants. However, there are a lot of problems here:

First, this is a remnant of the scala naturae and, just because of that, should be avoided. Think of it as a meaningless term, just like "more evolved organism".

Second, there is no clear and indisputable definition of what is a "higher" plant. Some authors used to define the "higher plants" as the Angiosperms only, or the seed plants (Angiosperms + Gymnosperms), or the vascular plants (Angiosperms, Gymnosperms and Pteridophyta). 

For instance, in lusophone biology books, it was very common a division in three groups:


lower plants: bacteria and algae;
intermediate plants: bryophytes and pteridophytes;
higher plants: gymnosperms and angiosperms. 


In those books, "higher plants" doesn't mean vascular plants, but seed plants instead. One could argument that those books use an incorrect definition, but my point here is exactly that the definition of "higher plants" is imprecise and wrong by its very nature: there is no correct use.

In conclusion: the definition of "higher plant" is not precise, and because it's related to a completely wrong concept, its use should be avoided.