This is not really true. Aside from ensemble models they tend to perform pretty much at par or better. Here's an extensive comparison by Rich Caruana [1]

[1] https://www.cs.cornell.edu/~caruana/ctp/ct.papers/caruana.ic...

Was this true, or perceived as true in 2003? My understanding was that people did not see them as performing worse than NN back then.

Definitely true. I worked for a company that was generating millions of dollars a year from neural networks in the mid 90s (edit: to be clear I didn't work there in the 90s, I joined years after their initial buildouts). The Unreasonable Effectiveness™ of neural networks has been true for a long time. When I worked there I tried switching out some models with SVMs and they were less accurate and took 1-2 orders of magnitude more time to train.

Really useful to hear, thanks! I know psychology was gaining a lot of headway with NN models in the 90s, but had little sense for what was going on in industry.