In the UK the main benefit in buying a primary residence property is the capital gains tax exemption if you were ever to sell your home. From an investment point of view this would depend how you structure your investments, are they in your own name, company, partnership, etc. The amount of debt taken on to acquire property could also play a role in your eventual tax bill. If you're looking to acquire property it is vital that you take professional advice.
If you are buying an investment property to let - in your own name - then you will lose out on mortgage interest relief if you are a higher rate taxpayer as the UK government is phasing this out. You can get round this by buying in a company but there are other issues to consider before trading through a company.
I am from Australia and there are very little tax advantages of owning a primary residence there. I never actually bought a primary residence. I always rented where I lived and bought investment properties. I ended up with 6 single family properties in Australia and still rented. I ended up moving to New Orleans and the fact that I rented made that transition super easy.