Do you have a source for this?

The cranial cavities are definitely larger, although it's ambiguous whether that just means better vision. No source on me, but it's not hard to find.

I had a quick googlefu about this (note quick). The articles I found seemed speculative and nothing concrete to show Neanderthals were smarter. Mainly showing they were more similar to us in tools/clothes but nothing to indicate more advanced/smarter.

I forgot to link to what I was thinking of: https://www.quora.com/Were-the-Neanderthals-smarter-than-the...

Although I had heard speculations of the sort through more reputable sources, I just can't find it at the moment.