Are there more Turing-unrecognizable languages than recognizable?
Yes, in fact one can show that there are uncountably many languages (say by representing a language as a sequence of the form $\{0, 1\}^\mathbb N$ which can be interpreted as the binary form of some real number in $[0, 1]$) while there are only countably many TMs (as any TM can be represented by a finite string), so almost all languages are undecidable, i.e. assuming we draw a language from an uniform distribution the probability of it being decidable would be 0.