Let's try and compare the two during their time as Jedi. This means not counting anything Vader did.
Anakin Skywalker
Pros:
+Trained from his youth
+Lived during a time when Jedi Knights were ubiquitous
+Competent general and leader
+Skilled with force abilities and saber combat
+Had the respect of those beneath him
+Young, but as capable as Jedi twice his age or more
+Able to think on his feet
This happens after his fall, but is still notable, as it indicates his innate talent:
+Is able to completely re-adapt his combat style after being crippled
Luke Skywalker
Pros:
+Had to rise as a Jedi without much formal training
+Shows innate skill with a lightsaber, learning how to use one in a relatively short period of time
+Takes the weight of restoring the Jedi Order upon his own shoulders
+Successfully converts Darth Vader back to the light side
+Overcomes his own inner demons and paves the way for the Jedi to reform and resurrect themselves without the faults of the old order
+Is able to reach new heights with the force, including force projection
+Never falls to the dark side
Who do you think is the better Jedi at the end of the day, and why?
Personally - and I'll elaborate on this later - I think Anakin was a more competent Jedi in terms of combat ability and intuition, but Luke was far more competent in understanding the concept of a Jedi Knight at its core and enforcing its spiritual philosophies. Which of those is more important to the question at hand I leave to you to decide.
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