Every voting system has pros and cons. It’s impossible to create a perfect voting system because there are multiple mutually-exclusive criteria by which a system can be measured.
So it’s important in such discussions to be forthright about which criteria you consider more or less important than others.
In order to avoid the spoiler effect and to discourage trivial tactical voting. To these ends, criteria like the Later-No-Harm criterion and Favourite Betrayal are important, but one need also look at the ways in which systems that fail them do so.
Approval Voting fails LNH trivially. In a genuine three-candidate race (i.e., one where prior to the election, you know all three have a genuine chance of winning) where your honest vote is to approve of Left and Centre and to disapprove of Right, but where you more strongly approve of Left, you are disincentivised from voting honestly because that will hurt the chances of Left winning. Unfortunately in so doing you also increase the chances of Right winning, compared to if you voted honestly. Basically, you’re forced to make a decision between your honest vote which increases the chances of a mediocre result, and a dishonest vote which increases the chances of either a very good or very bad result. It’s LNH because you’re incentivised to not vote for Centre even though you honestly would have.
In IRV you get a similar outcome in theory, but what we’ve seen in practice is that it doesn’t actually play out. The difference comes down to how preferences are distributed and who gets eliminated. If Centre ends up coming last on first preferences, that’s where Favourite Betrayal comes in. In your honest vote, Centre’s preferences distribution is entirely up to those who voted Centre, which could be a mix of Left and Right, which risks Right winning. If you had voted dishonestly and put Centre ahead of Left, you’re increasing the chance that Centre isn’t eliminated first, and instead Left is, with Left votes going to Centre—a better outcome than Right winning.
But the thing is, in practice this doesn’t tend to be the case. I live in a seat where this happened in our election last year, and it turns out that people who vote for one candidate overwhelmingly tend to second preference the same candidate (at least once smaller non-viable candidates are ignored). The Australian Greens (Left) and the Australian Labor Party (Centre) actually preference each other at the same rate. And so it came down to the fact that Labor was eliminated first (after non-viable candidates) by a very narrow margin, giving almost all their next preferences to the Greens, resulting in a Greens win. Not voting strategically, in the real world, actually pays off under IRV. Under Approval, because the ability to actually express your nuanced preference doesn’t exist, tactical voting is more strongly encouraged. In summary, while LNH and Favourite Betrayal are, in a sense, “equally bad”, the former is more of a problem when looking at the real-world preferences of voters, and a system which fails the latter should be preferred over one that fails the former.