I think it depends on where the topic is being taken. If you're talking about the very top echelon, then everything is a prerequisite (domestic dominance, amassing huge numbers against fodder, etc., etc.) but the defining moments are the biggest games on the biggest stages.
When we think of domestic legends, it usually in relation to what they did in "big <insert>" games rather than smashing the remainder of the league to smithereens. Those plaudits come more readily when the player in question proves time and again that they are king of the hill and either peerless or peered only with those players who can hang, and do the very same. Another truth with regards to these discussions is the big games have multipliers on them that the "little" ones simply cannot.
Giggs and Gerrard share a similarity in that they had most of their best games against the higher profile opponents whilst not being as stellar against smaller foes - Giggs was a legendary performer in the CL against the very best FB's in the world (his games against Zanetti being particularly legion), but he wasn't outputting at that rate so often in lower level games. Gerrard's reputation is more due to what he did in big games (not against us, and Keane!), but against others of a certain stock, or even being 'the man' when needed against those smaller fry.
If you're a bona fide performer in the CL, it means you are the best of the best in club football, so obviously that is the platinum standard. If you were to tier it, the big <insert> games in domestic leagues would be gold, middling games silver and the fodderish stuff bronze. There's a few famed stories about some players of elite standing who didn't/couldn't get up for the bronze and silver stuff, but come the gold or platinum, they would be the best players on the pitch, bar none. So it's a web within a web, but domestic football has more caveats than the other stuff, as every top player is trying their utmost at the latter stages of the CL, if not for the trophy itself, then for the personal glory and esteem performing in those latter stages does to a career and legacy.
All games are to be enjoyed by fans and performances lauded, but there is no question at all regarding the clear divides between what great is in terms of relativity. Your post is correct in that the body of work for some players seems to just be washed away or recalled selectively. Not thinking too deeply about this, but Keane is still the top of the totem as the most dominant from fodder (bronze) through to the best there is/was in club football as far as the PL goes. C.Ronaldo too. It's interesting to see how Lampard is played down in this regard despite being another whose club career is virtually flawless in terms of consistency 'across the realms'.
