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DSLR autofocus is reliable, especially with tracking. Actually, they're reliable in every aspect. It's more than enough for everything you could think of doing with it, and then some. It's just not convenient to carry around because of their size and weight, and they can get loud.
Mirrorless cameras are smaller and less conspicuous, but that comes at the cost of performance in areas that could be dealbreakers, like slow start-up time, software bugs, unacceptable noise, AF performance, etc. There are some exceptions to this rule, though. A mirrorless is what you take if a reflex camera is overkill.