Given the precision of electromagnetic instrumentation, it is often easier to detect charged particles than non-charged particles.
Also, perhaps more importantly, most Higgs boson decays have large SM backgrounds from other processes that look similar to Higgs decays. In contrast, a top decay is more distinctive with fewer similar processes to create background. The diphoton decay of the Higgs was critical to its discovery, even though it isn't a particularly large branching fraction of Higgs decays, because it has a much smaller SM background than the more common Higgs decays.
And, unlike the Higgs for which theoretical alternatives were being discussed right up to a few months before it was discovered, there was no viable theoretical alternative to the top. Once a third generation fermion was found, the exact properties of the top, except mass and CKM matrix entries, were overwhelmingly clear and the mass and CKM matrix could be guessed within boundaries from existing data. We knew that the CKM matrix entries for top to strange and top to down had to be vanishingly small and we had a lower bound for the top mass. So there was a pretty clear and more importantly undisputed among physicists, target to search for. A clear target makes it easier to design narrowly tailored searches for what you are looking for in a more efficient way.
