You're never sure which will have a better combination of antenna and tuner. It's not just the tuner that matters, you have the antenna and location of the setup that matters.
I think a lot of folk didn't live with antenna from the 50's to 80's or have forgotten.
So, no. You can't make this assumption.
Recently cut the cable on TW and installed a HD antenna in my attic.
I networks to 6 TVs throughout the house. All receive a mix of TV channels but the largest TV (55"Sony) seems to get more. All things being equal does size matter or does the larger TV have a better built in tuner than the others.

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