Is equivalence of unambiguous context-free languages decidable?
This is currently an open problem.
As correctly pointed out, if it is decidable, then one expects the proof to be hard since it generalises the famous DPDA equivalence problem.
On the other hand, the classical arguments for undecidability of the CFL universality problem make use of inherently ambiguous languages, and thus one needs new ideas to show undecidability.

Let me point out that the universality problem for UCFLs is decidable (in PSPACE), using generating functions [1].

REFERENCES

[1] N. Chomsky and M. P. Schützenberger, The Algebraic Theory of Context-Free Languages, Computer Programming and Formal Systems, 1963.