Every portfolio of investments should contain a combination of the two with international shares being spread across many different regions around the globe. If not, you are potentially missing out on good returns.
Some of the key factors to consider are:
1) UK shares eliminate the currency risk because your investment is made in GBP
2) Some of the biggest UK companies earn a lot of their profits from overseas so UK shares are not pure UK investments
3) International shares provide pure exposure to different markets around the world
4) International shares include high growth areas such as Emerging Markets and Asia
5) Developing markets tend to be more volatile than developed markets