It depends on what you mean by "better". Here are some factors to consider:
Screen size: A projector can often project an image much larger than what you would see in a typical cinema. This can make for a more immersive experience, especially if you have an empty wall and sit close to it.
Picture quality: Some home projectors today can produce high-quality images, and they are able to match the image quality of a high-end cinema projector in-room environment. Cinema projectors are designed to produce very bright and detailed images for large capacity, and they are often calibrated by professionals to ensure the best possible image quality.
Sound quality: Cinemas usually have high-quality surround sound systems that can create a more immersive audio experience than a typical home theater setup. However, with the right speakers and audio equipment, it is possible to achieve excellent sound quality with a home theater projector.
Convenience: With a projector, you can watch movies in the comfort of your own home without having to leave the house. You can also choose what you want to watch and when you want to watch it. However, going to the cinema can be a fun social outing and can be a great way to experience new movies on the big screen with a crowd.
In summary, a projector can be a great option for home entertainment, especially if you want a large screen and the convenience of watching movies at home. However, a cinema can offer a more immersive audio and visual experience, as well as the social aspect of watching movies with a crowd. And if you enjoy privacy with special someone, why not a home projector?