Trade prints tell you where business happened; quotes tell you where you could have done business. For any strategy sensitive to the bid-ask-spread, quotes are the honest basis for fill modelling, because buying at the last trade price is often not possible.
Consolidated quote feeds show the national best bid and offer but not the depth behind it. A 100-share quote at the top does not mean your 5,000-share order fills there, and backtests that treat the NBBO as unlimited size overstate results in small caps dramatically.
Timestamp alignment is the recurring pitfall. Matching a trade to the quote in effect at that instant requires both feeds on the same clock, and vendor clock differences of a few milliseconds are enough to make every trade look like it happened at a favourable price.
Related: tick-data, bid-ask-bounce, timestamp-alignment, fill-assumption