While I think Frankenstein is a better horror movie, I think Bride is a better film in general. But Universal monsters needs a place - there are just too many horror film tropes it spawns.
As mentioned upthread, Young Frankenstein is almost a complete recreation of Son of Frankenstein - same exact plot, characters, the Inspector with the artificial arm, etc. Watch Son, then Young Frankenstein. YF copies some scenes from F and Bride (the child, the blind man etc), but the plot is SOF. It's like watching Zero Hour then Airplane.
Glad to see the theme of Frankenstein wanting to create life while ignoring his wife -- while ignoring the very thing which naturally allows him/them to actually create life. Also, the theme in the book is about not escaping the results of our prying into natures secrets, not "secrets we were not meant to meddle with" which is one of the film's themes. Yes, we can create life, built an atomic bomb, clone dinosaurs etc - but they don't go away.