IMO: Led Zeppelin (late 60s) > Rolling Stones (65-70) > Pink Floyd (67-73)> Eagles
1971-1976 The Eagles had more hits and out sold all of the above.
On the more general point of "Top band of the '70s", I think you'll find it a very hard case to make on the metrics you're choosing. Even for the more limited case of '71-'76, they're not the top in either hits or albums sold.
Some perspective on hits, using Billboard Hot 100 numbers from 1971-76:
Group | Top 100 | Top 10 | Number One |
The Eagles | 12 | 6 | 3 |
The Rolling Stones | 13 | 4 | 2 |
America | 13 | 6 | 2 |
Wings | 14 | 11 | 4 |
Three Dog Night | 13 | 7 | 2 |
The Bee Gees | 12 | 6 | 3 |
Elton John | 20 | 15 | 6 |
Stevie Wonder | 13 | 8 | 4 |
(Not counting Another Day or Uncle Albert/Admiral Halsey for Wings.)
As far as the bands I mentioned: yes, at their peak, the Eagles edged out the Rolling Stones for hits. They were comparable to the Bee Gees, before the Bee Gees peaked.
Album sales: Led Zeppelin IV sold 23x platnum, while The Eagles' five studio albums up to 1976, taken together, sold 25x. Then you have Zeppelin III (6x), Houses of the Holy (11x), Physical Graffiti (16x), Presence (3x) and The Song Remains the Same (4x), totaling an additional 40x. The Eagles put their greatest hits out in '76, and that went to 29x, but they still fall 9x short for the period. And that's if you feel good about counting a greatest hits album, just because it happened to come out in the period we're talking about.
I was really commenting on the "volume and quality" bit, though, which doesn't say "sales" or "hits" to me. If you think The Eagles' quality in that period blew away Led Zeppelin's, we're just working with very different yardsticks.