How wary should I be of old cosmology books?
It's a sliding scale. Generally the older the book, the more the chance of something being wrong. But it depends what books you're talking about. Are they text books? Or are they popscience books? Some books, even newish books, have a habit of presenting speculation as established fact. There's been a lot of trouble about inflation and the multiverse recently. Peter Woit talks about it on his Not Even Wrong blog. He says “the political campaign for the multiverse continues today with a piece by Amanda Gefter at Nautilus. It’s a full-throated salvo from the Linde-Guth side of the multiverse propaganda war they are now waging”.
I know, from a recent book, that the inflaton theory is probably newer than both books
Inflation started in circa 1980. Guth coined the phrase and generally gets the credit, but it arguably goes back to Erast Gliner in 1965 and his paper algebraic properties of the energy-momentum tensor and vacuum like states of matter. It didn’t get much attention.
and that the Higgs Boson has been discovered
When inflation was first mooted Alan Guth talked about the Higgs field and GUTs, saying magnetic monopoles were "topologically stable knots in the Higgs field expectation value”. But that was old inflation, which was replaced by new inflation, which was replaced by eternal inflation. As far as I know the Higgs field is not thought to be linked to the inflaton field.
Has anything else changed since then?
Yes, like pela said, before 1998 people thought the expanding universe was slowing down. There are other changes too. Some people used to say the universe was once the size of a grapefruit. Now since WMAP some people say the observable universe was once the size of a grapefruit, and the universe is infinite. For myself I cannot see how that fits with big bang cosmology, which I think is largely correct.
Which topics of the books should I understand are considered outdated?
It's hard to say. Dark matter, dark energy, cosmological constant, flatness of the universe, size of the universe, age of the universe. If you could name the books maybe I could look at the chapters.