Without any second thoughts, I consider IIT Bombay a much better option than IIT Delhi. Some reasons that speak in favor of my opinion are

• IIT Bombay enjoys a higher locational advantage as well as a better-equipped campus.
• While both IITs have a decent Research culture, IIT Bombay is at a level higher than IIT Delhi in this aspect. It has a larger number of Papers and Patents to its credit.
• The ambiance at IIT Bombay is rather chill with no strict rules and regulations. You are free to do anything and no restrictions are imposed on dress code or LAN.
• IIT Bombay has a better climate than IIT Delhi.
• IIT Bombay enjoys the advantages of being a Financial capital with additional opportunities for the non-core sector.
• IIT Bombay has a few BS programs like BS Economics, Mathematics, and Chemistry which are not present in IIT Delhi. These programs are a bridge between engineering and applied science and render a wide scope of research and at the same time, applied fields.
• IIT Delhi has extra BTech programs like BTech Textile, BTech, and BioTech. The students of these programs usually go for non-core jobs and corporate life.
• IIT Bombay welcomes a number of eminent personalities. Some recently invited personalities include PM Narendra Modi, Brett Lee, Sadhguru, Yami Gautam.
• IIT Bombay has amazing hostels for freshers.

So both the institutes are elite in their own essence but nowadays IIT Bombay is a clear winner between the two.