I lived in Quebec City in the late 1980s and was raised a Nordiques fan, then transferred my allegiance to the Avalanche when they moved. So I watched the entirety of both Sakic's and Forsberg's career.
I think both players are amongst the best to ever play the game. I don't really get caught up in rankings, but in an all-time sense they should be reasonably close to one another.
I don't think there is a clear black and white answer here that everyone is looking for. Firstly, no one should dispute that Sakic had a longer and more productive, and a "greater" career than Forsberg. However, I think its fair to say that Forsberg, when available, was a more consistent performer in the regular season and playoffs - particularly in the late 1990s. Disregarding the injuries (I'll get to that later), Forsberg didn't have the "lows" that Sakic did from the season-to-season or playoff-to-playoff. But, he didn't have the "highs" that Sakic did either - Sakic had the best regular season between the two (2001), and the two best playoffs (1996 and 2001). When Sakic was able to put it all together, like he did in 1996 (most fans sleep on his 1996 regular season, which was outstanding as well) and 2001 (which was one of the most dominant full seasons in recent NHL history) he performed at a level above Forsberg's best. The issue with Sakic then, was consistency. Forsberg had the consistency in performance, but unfortunately not the availability...for long stretches of his career.
In terms of skills, Forsberg's skills were more visible and jumped off the page more than Sakic's; Forsberg was dominant with the puck, very physical, an elite passer, hungry, determined, and wanted the challenge of taking on the opposition's best defensive players. Sakic's sills were much more subtle and nuanced. You wouldn't notice Sakic, for stretches of the game, then before you knew it the puck was on and off his stick and in the back of the net. Most casual fans with a basic understanding of the game would probably notice Forsberg quicker and his play style would resonate with them more than Sakic. I just think they were very different players, and their playstyles matched their personalities. Sakic was a quiet, humble dude. The proof is in the numbers and results though, and Sakic was one of the most productive players in NHL history.
Sakic also had a clutch factor that set him apart from his peers. In the biggest games of his career, he was the best player on the ice. 2001 Cup finals, game 7, with Forsberg injured, backed by a 2nd scoring line featuring Hinote, Drury and Niemenen, and while being matched-up against by Stevens and Madden (amongst others) Sakic goes 1+2 = 3 to lead the Avs to the Cup on home ice. 2002 Olympic gold medal game, Sakic goes 2+2 = 4 and is the star amongst superstars to lead Canada to the gold medal. In one game, winner takes all the marbles, give me Sakic.
My view is that Forsberg can fairly be considered the "better" player, in the sense that he was more skilled. It depends on the observer, I think. Forsberg probably had a more unique skillset, was a more unique player, was more consistent at a high level across his career. Sakic played a lot longer, played at a higher level intermittently, rose to the occasion in big moments, and was a member of the franchise his entire career.
Overall, imo Sakic is the greatest player in Nordiques/Avalanche franchise history.