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The built-in tuners of TVs are certainly more convenient since there's no need to switch back and forth between different inputs.
Furthermore, if your TV is able to display 720 or 1080 native resolution, then you'll get a better picture when the stations are broadcasting HD content. The external converter box (the $40 variety) can only put out S-Video, composite video, or RF channel 3/4. None of these formats can handle anything above 480 resolution, so any HD content will be converted to a 480 resolution before being sent to your TV.
However, to answer your question, I've found that external converter boxes usually do a little better on specs such as Noise Figure. That means if you've got some marginal channels, the set-top box might do a better job picking it up than the TV's tuner. If all of your channels are strong, then you won't notice any difference in terms of number of channels received.
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