It's not up to the aperture, it's up to the method how the lens focuses.
The most of older (and not so old) (D)SLR lenses use unit-focusing method, they move the whole optic group to focus, while modern mirrorless lenses focus by moving only one lens, or just a small portion of the lens optics. Moving only one (or a few) lens(es) is much faster method than moving around the whole optical group of a lens, so it is expected that the unit focusing method would be slower - and from practical experience, I can say it most definitely is.
The vast majority of mirrorless lenses use the second method (moving only one lens) to achieve fast focusing speed, the only exceptions I can think of are the first two microFourThirds primes - Panasonic G 20/1.7 and Olympus M.Zuiko 17/2.8, both use a classic DSLR-style unit-focusing method. I've had 20/1.7, it was focusing slower than any other lens in the system, especially when compared to 25/1.4 or 45/1.8 lenses, and all those lenses have a large aperture.
Shallower depth of field should be easier for CDAF - there's more difference between what's sharp, and what isn't. On the other hand, any loss of contrast and sharpness many older optical designs have is a disadvantage.
It is not unexpected that EF50/1.4 DSLR lens focuses slowly - that's as a classical SLR-style lens as you can get, it is designed in 1993, in the film era while autofocus was still relatively new technology, in the time when nobody was pixel-peeping, and great sharpness wasn't expected at wide apertures.