Firstly, there is no such licence as an ICAO licence. ICAO set (or recommend) standards and recommended procedures/practices and as such an FAA, U.K. CAA and EASA licences are ICAO compliant - as are most other countries.
The two most widely acceptable licences are FAA and EASA but most countries will “validate” an ICAO compliant licence for use for a limited period and allow conversion with limited study/testing. That may change once the U.K. CAA re-establish a reputation within the industry (cough)!
So, as has been said, it more boils down to your nationality, where you can live and work, or where your spouse is from.