Khana khati hoon, is better than other.

I think both are pretty much similar. Khaana khaati hu is more prevalent as it is "more" colloquial than bhojan karti hu

Both are same but it depend upon us what we want to use...

Actually "खाना खाती हूँ"..we can use it then we someone ask you what you eat then you can reply (khana khati hmm)....

"भोजन करती हूँ" we can use when someone ask you "what you do at afternoon." then you reply (bhojan karti hmmm)....

but remember both are correct. it depend on situation how you reply.

Actually "Bhojan" word is come from Sanskrit. "Khana" word is a urdu word.

When When Mughal(Muslim) empire established in india. Ruler force to use urdu Language and slowly slowly people became habitual of some word..So "khaana" word came into the light between people. 

So in sort Native word is "Khana" word . But if you want to use pure Hindi then you can use "Bhojan" word .