Yeah, this is why longevity is so important, particularly if (like me) you put a lot more importance in a player's overall career than his peak.
The ultimate example is the hypothetical batsman who averages 70 over a 10-year career, then declines to a point where he's only going to average 50 for the next 10 years if he plays on. He'd definitely go down as the better player in my book if he played on, even though he'd average less, as he's still producing a positive output to his team by playing, and the change in career average wouldn't change the actual output of the previous 10 years. As long as you're performing to a better standard than the 12th man could, you're only adding to your resume even if your average is decreasing.
Anderson (who is the ***, I should add) may average more than Sidebottom but, as you say, that's comparing apples with oranges as Sidebottom wasn't forced to play outside his peak. Sidebottom's career is a sample size of his best (and only) 22 Tests and in that time he took 79 wickets at 28. Anderson's best period of 22 Tests was between May 14, 2009 and January 26, 2011 in which he took
96 wickets at 25. Recognising that isn't really prioritising peaks in that way that someone might if they preferred Botham to Imran, but it recognises that Anderson clearly has Sidebottom's career covered, particularly when you add in all those other Tests in which he was deemed good enough to play for his country and performed to a decent even if often underwhelming standard.
I don't consider myself a peak man at all; the DeusEx idea that cricket is only about achieving the highest level of skill possible and to hell with how useful you are to your team across your career seems absolutely absurd to me, but that doesn't mean I don't like to break down performances in time periods and acknowledge that players improve and decline. That Sidebottom wasn't selected outside of his peak doesn't make him a better player than Anderson, for example, as Anderson was of more use to England when he was blowing out his average than Sidebottom was when he wasn't playing at all, and he was more useful during his best 22 games (the entire length of Sidebottom's career) as well. It only really gets confusing when you compare a short career to a long one and the long one doesn't actually have a segment in it as good as the short one; then it's really a balancing act in deciding which was more useful.