Until I started studying hockey history, my impression was Maurice Richard was the better goal scorer by a clear margin. Sure, Howe had a higher career total, but that didn't necessarily prove anything. Mike Gartner had a higher career total than Mario Lemieux.
It didn't take me long to start questioning that notion. What immediately stood out is both men won five goal-scoring titles. (In fact, Howe led the league in goals five times under "normal" circumstances; one of Richard's titles came during WWII, when talent was depleted). And through 18 seasons, they scored nearly the same number of goals (Richard was up 544-540). Howe's immense longevity helped him push his career totals even higher, but he didn't need freakish longevity to surpass Richard's total. Howe had almost as many years in the top three in goals as Richard had in the top ten (12 vs 13) - yes, part of that is a reflection of longevity, but it isn't like Richard had a short career (he retired 2nd all-time in games played).
I think the general perception that Richard's a better goal scorer than Howe is due to a combination of factors (from weakest to strongest):
Good marketing - when Richard died in 2000, the NHL introduced the Rocket Richard trophy (a statistical award, going to the player(s) who scored the most goals in a season). It's likely that this has influenced fans who are, say, 30 and younger (since goalscoring has been synonymized with Richard's name). But I don't find this explanation compelling, because the perception that Richard was the better goalscorer predated Richard's death.
"50 goals in 50 games" - most hockey fans know that Richard was the first player to score 50 goals in 50 games. Anyone who's studied pre-expansion hockey knows that this took place when the league was depleted, as most players had joined the armed forces during WWII, and Richard's competition was predominantly minor leaguers. (Just two years later, Richard scored 45 goals in 60 games against a full-strength league, and this is generally considered a more impressive accomplishment). But most casual fans don't know this, and Richard has a "signature" goalscoring factoid, while Howe doesn't. (People are easily impressed by round numbers, and pretend that 50 goals is significantly more impressive than 49, or that 501 goals are significantly more impressive than 498).
Specialization - Howe was a better playmaker by a wide margin, and also better defensively. The men were rivals on the ice (though, as Howe discussed in his biography, they eventually became friends in retirement). There may have been an attempt, even subconsciously, to exaggerate Richard's goalscoring ability in order to make this a more compelling rivalry. If Richard wasn't clearly the better goal scorer, what else did he have?
Sniper vs shooter - we only have SOG data for his final season, but by all accounts, Richard was a sniper. He scored many of his goals on breakaways, and was known for his accuracy. Howe was clearly a volume shooter. (We have SOG data starting in 1960; over the next eight seasons, from ages 31 to 38, he was first or second in shots on goal each year). Just as we've seen with Ovechkin, perhaps some criticized Howe's goalscoring ability because he "needed" to take so many shots. (I've explain before why I disagree with this reasoning, but it's conceivable that this was an argument against him).
Playoffs - I think this is the strongest argument in favour of Richard. He's probably the 2nd or 3rd greatest playoff performer in NHL history, and that's almost entirely on the strength of his goalscoring. He outscored Howe 82-68, despite Howe having played in 25 more games. (That's 0.62 vs 0.43 GPG - a huge difference). The counterargument is Howe had several deep playoff runs before he entered his prime, which dragged down his average (Richard didn't play in the postseason until he was 22, and the league was depleted during those first two runs, where he scored more than goal per game). But even if you play around with which years to include, Richard comes out ahead. (Plus, Richard remained the all-time leader until the mid 1980's, which is incredible considering the playoffs were only two rounds back then). He's still 8th today, 64 years after his final game.
Richard was pretty clearly the better goal-scorer in the playoffs, but I think the reputational gap (at least among casual fans) is exaggerated. Someone would have to place a heavy emphasis on the postseason, and little to no emphasis on consistency and longevity, for Richard to rank higher. (I'm not saying that can't be done, but it should be applied consistently - someone that ranks Richard above Howe would probably rank Bossy relatively high, and Hull and Ovechkin relatively low).