I've heard the phrase "miles better than..." being used. A quick Google search will return results for "miles better than...", but there's no result where the phrase "light years better..." has been used. As both are a unit of measuring distance, can "light years better..." be used as it is analogous to "miles better..." or is "light years ahead..." the only acceptable way?
Both miles and light years are measures of distance and therefore 'ahead' is the most appropriate usage. However we do say 'far better' where far is admittedly a substitute for 'a lot' and no reference to distance anyway.
Thus 'miles better' is just another way of saying 'much better' or 'far better' and your argument for using 'light years better' instead of 'miles better' is actually valid -- moreover if you were to say 'light years better' rather than 'light years ahead' it would be grammatical and might even remain idiomatic; and I am sure your listener would get the correct meaning.
Having said that, let me remind you that 'light years ahead' is usually used as a measure of progress:
EL and U is light years ahead of other websites in the matter of keeping discussions on topic.
Literally, ELU has progressed far ahead of others, by a measure of light years (hyperbolic, as already noted in an earlier answer) and that is a sound reason to use 'ahead' in preference to 'better' in such a construction.
With "miles better" vs "miles ahead", "miles better" doesn't really make sense: I'm not sure if it's actually ungrammatical but it's certainly semantically a bit broken. So, "miles better" is more colloquial, or informal.
Given this starting point, "light years better" seems even more broken than "miles better", in a way which most people would find a bit confusing. Colloquialisms generally only work if people are familiar with them - inventing your own is risky.
"Light years ahead" is obviously hyperbole, but it makes sense, logically/semantically, and so I think is less likely to confuse people. Also, some people probably do think that a light year is a unit of time, and for those people "Light years ahead" would also still work - it sounds like "Much more advanced".
So, I'd go for "light years ahead".
It's an idiom so it really comes down to colloquial usage. You've identified an interesting mistake we have all been making as a society! Merriam-Webster has an entry for only "light-years ahead" and uses the hyphen, which makes "light years" into a compound noun. When I search for "light years better" nothing comes up.
So use it as if you are saying "years better."