Kyoto is a more touristy destination and a cultural melting pot. This is why accommodation and food tend to be more expensive here. If you're on a budget, I highly recommend visiting Osaka. The city is a nice mix of culture, nightlife, and great food.

Is it better to stay in Kyoto or Osaka?

Kyoto has far more popular or historical sites, shrines etc. If you are into those, then you should spend more time there than in Osaka. Osaka has more vibrant night life. It will be harder to experience if you need to go back early and catch last train.

What is the difference between Osaka and Kyoto?

Kyoto is more culturally immersed as it is the ex-capital where as Osaka is more for commerce developed from the old merchant town. Osaka is good for a day or less(mainly eat & drink) but Kyoto for 3 or more days. If you can find a hotel room, stay in Kyoto. You can commute but may get tired & miss out on night scenes.