Hedgehog
Hedgehogs rank among the most universally beloved creatures on the British Isles. Their combination of apparent vulnerability, endearing snuffling sounds, and comically ineffective attempts at threatening behaviour render them irresistible to humans of all ages.
Wildlife rehabilitation centres report that hedgehog patients receive significantly more visitor attention than other species, and children's literature has capitalised on their inherent charm for over a century.
Godzilla
Approaching Godzilla is, by most reasonable assessments, inadvisable. The creature's mere footsteps register on seismographs at considerable distances, and its body temperature has been measured at levels that would sublimate human tissue upon proximity.
That said, certain iterations have demonstrated a protective stance toward humanity, and the 1960s films featured the creature performing what can only be described as a victory dance. Approachability varies considerably by continuity.
VERDICT
One may safely permit a hedgehog to investigate one's garden; permitting Godzilla to investigate one's garden would result in the complete absence of garden, house, and likely postcode. The hedgehog's substantially lower lethality radius renders it the more companionable option.