It's well known that greater variance in letter height aids readability since it makes letters more distinct. In this case your problem is the Ascender Height vs the X-Height (or possibly the Cap Height).
The readability of All Caps text has long been known to be poorer than normal type, mostly because the lack of variation in letter forms. Mixed Case is more readable because the height and shape of letters makes it easier to distinguish individual letters. For example, any letter with an Ascender or Decender is easily recognizable when skimming over Mixed Case type, but if all letters are at or near the same heights (as they are in All Caps) they are more difficult to distinguish.
From Tinker, Miles A. (1963):
Writing Systems, A linguistic introduction (Sampson, Geoffrey (1985)) also mentions that ALL CAPS fonts are harder to read than Mixed Case, which is why British Road signs now use mixed case.
This related question All capital titles: good or bad? has some good relevant resources, though it also focuses mostly on All Caps, not differences in ascender height, but some of the referenced findings are still very relevant.
I too have never heard of any term named "L height". I take it to mean cap height, ascender height or line height, and your question to refer to the ratio of the typeface's x-height to any of the above.
A taller x-height (relative to the point size) improves readability at small sizes since it opens the counters (the holes in characters like 'o' and 'e'). That's what makes Verdana so terrific at small sizes (especially on screen with the great hinting it has). A font with a very small x-height like Futura is generally less readable for copy text and generally benefits from more whitespace and sometimes all-caps.
Readability is a very complex topic though, since there are so many factors that affect the readability of a piece of text. Print vs screen use is high on the list. Even on-screen, a high-DPI display like the one on the newer iPhones is a wholly different beast than older, 72- or 96-DPI displays. The copy you're typesetting affects readability, as does the point size, leading, tracking and measure (block width). The weight of the text and the context of the reader (at home in bed vs. reading a poster at a bus stop) also have a huge impact.
The short answer, as with pretty much every typography question, is "it depends".