Anyone who has ridden on both a Bury Line 504 and the NY Subway within living memory would emphatically agree with
@Sun Chariot that there's no comparison!
But it might depend on when that comparison was originally made.
If we're talking about the L&Y's initial electric stock from 1916 versus early NYC subway cars from about the same era - there may have been more similarities. The Subway stock back then was still quite utilitarian but more lightweight and a lot less metallic and "bomb proof" than the trains introduced from the mid-20th Century onwards.
For example, the IRT Composite cars of 1904 vintage:
commons.wikimedia.org
commons.wikimedia.org
Compared to the look of the 1916 Manchester - Bury stock - seen part way down
this page of The Lancashire & Yorkshire Railway Society's website.