I've been meaning to put up this sort of comparison for a quite some time, so that it is perhaps clearer why I have been thinking about designing a symbol font to serve as a better companion to AMS Euler.
Above is an excerpt of a side by side comparison of AMS Euler and Computer Modern Italic (which is the Computer Modern math font) that I just prepared. For the most part it is hopefully clear that AMS Euler has a generally darker »color« and more »robust« stems. Now consider a comparison of an inference rule not unlike would be seen in many papers I read or write.
The important points to note here are that currently, many important symbols are used identically regardless of which typeface has been chosen. Therefore, despite AMS Euler's darker color the turnstile, equivalence symbol, up-arrow, and »forall« quantifier remain the same »weight«. It is interesting to note that the up-arrow is ever-so-slightly wider for AMS Euler though. Additionally, in this context it feels like the universal quantifier should have a wider spread when used with AMS Euler. The star probably is fine as is, but it might even be worth providing a heavier version.
Anyway, I hope this makes things clearer. However, if you disagree with my assessment, and feel that the differences are insignificant, let me know that too.