I believe that anti-Protestantism or anti-evangelicalism (like anti-Catholicism) is also a vast and disturbing social problem, coming largely from the left, the media, academia, and the entertainment industry, and including also the usual prevalent bias against "Southern conservative white guys" who are invariably stereotyped as troglodyte anti-intellectual fundamentalists -- the portrayal of the Scopes Trial, e.g., is a quintessential instance of this (and this itself is part of the common Northern bigotry against the South: and I say this as a Michigander, though one of my grandfathers was born in Alabama).
As to the relative prevalence of both, I don't have any particular strong opinion, nor do I think it matters much. The important thing is for conscientious Christians to condemn both.
That said, I would note that the official Catholic position is to acknowledge Protestants as Christian brothers, whereas many Protestant groups either are officially anti-Catholic or contain within themselves a strong legacy of anti-Catholicism which is then passed down almost unconsciously.
Therefore, I would suspect (though I don't assert) that anti-Catholicism is the more prevalent of the two, simply because it is fed from an important and influential sub-stream of Protestantism as well as from the secular and leftist worlds, which would seem to me to despise both of our camps alike.
Individuals, of course, might fall short of properly informed and charitable attitudes, just as they do concerning ethics or theology, generally-speaking. The difference with the Catholic, though, is that if he rails about Protestants being non-Christians, he is going against the express teaching of Vatican II, which is binding on all Catholics, whereas when Protestants do the reverse, they are in a quite respectable Protestant tradition which can easily be traced right to Luther and Calvin themselves.
So they are arguably in the mainstream of their tradition, whereas Catholics must violate their actual tradition to do the same thing. For example, Feeneyites may claim Protestants aren't Christians, but they have been condemned by the Church itself as an erroneous fringe group.
I suppose this is enough to arouse ire against me, but again, I reiterate that I think anti-Protestantism is an extremely serious social problem and acceptable prejudice as well. If anti-Catholicism is a greater problem, it is only because it is so often generated by fellow Christians and not simply secularists who are nominal concerning, or outside any brand of Christianity whatsoever.
I should clarify that secular anti-Catholicism and anti-Protestantism both are more in the nature of a "sociological derision" -- we are opposed because of our stands on traditional morality or because of political conservatism, or (above all) opposition to abortion and the Sexual Revolution, homosexuality and so forth.
The secularist doesn't care enough about doctrine for that to be any issue for them. They would acknowledge both camps as Christian: they simply don't like us (we're "lousy citizens" who aren't playing the game the way it should be played). It is all social issues for them and intolerance for the counter-cultural aspects of any form of solid, robust, life- and culture-transforming
One should note the different definition, then. My standard use and definition of "anti-Catholic" and "anti-Protestant" both, is the mistaken and self-defeating view that those groups are not Christians. The Protestant anti-Catholic may also despise some sociological or non-theological aspects of Catholicism, but that does not enter into my own use of the term, as I have stated many
The secularist, on the other hand, is usually not concerned with theological categories or content. It is a more pure prejudice, based on mere disagreement and dislike, because many Christians are not good social liberals and cause too many problems and inconveniences.
At least the educated anti-Catholic Protestant usually has some principles of theology that he thinks (either rightly or oftentimes wrongly) that the Catholic Church opposes. They are right when they say we oppose sola fide and sola Scriptura; wrong when they claim that we oppose sola gratia. It is just as wrong, and it is just as wicked, but at least they think they are upholding some better good (true theology and the following of Christ), whereas the secularist has few noble motives at all in his anti-Catholicism or anti-Protestantism, whatever the case may be.