Which microscope is better? Olympus or Nikon? What are the differences between Olympus and Nikon stereo microscopes?

Olympus and Nikon stereo microscopes are similar by features and price. Most popular brand in microscope is Accu-scope, Meiji and Vanguard. I have given a link below where you can find a PDF file. You can download and compare features. Thanks.

I was interested in Microphotography and was told while enquiring about microscopes that the most important factor to watch out for was the light source.

It depends again. on what your expectations are and what you hope to achieve, if it's just something to experiment with then you might not need a top spec microscope, if it's for something serious then your investment should reflect that.

They are both very similar in performance.

But the better microscope is a Carl Zeiss; go for one of them.

They're the same. They're just tools. Both have excellent optics though.