I have lived all my life in Delhi & spent about an year in Mumbai, so I think I've a different perspective of looking at this "rivalry".
My house (Paternal, I was born here & my Father before me & live in a Joint family) in Delhi is big, spacious & most of the bedrooms have attach lat/baths.
I craved for space in Mumbai, although my consulting gig paid well in stock & bonuses & I was getting a 12k HRA it barely covered my rent. I got a small ground floor 1BR + Small kitchen/store room for that money in Andheri East, which apparently was only 5 minutes walk from my office in Mahakali Caves Road (Near Tunga Restaurant).
I had a small fenced verandah & space to park my car, which although didn't had a society sticker was still had empty spot.
I loved my empty parking spot but hated the room; it was tiny & it sucked the life out of me, I didn't even have space to put in a real bed & accommodate a cupboard, the place came with a godrej almirah but we all know how much do we use those, I improvised used a futon mattress & got myself a industrial rack from my designer friend.
The love affair with my apartment didn't last long since it was on ground floor it almost drowned in Mumbai rains, I had to sleep on a friends couch for a week & almost got my things ruined hadn't it been to nice uncle who noticed the rains doing damage & informed me. I cut short my trip to take charge.
Still Love The Parking Spot:
I still loved the parking spot, I live in South Delhi & still hate to find a decent one near my home, apparently we own too many cars for one household to sustain healthy parking ratio (perks of living in a Joint Family, you will always be fighting for that golden spot with your elder cousin)..
We The People:
The people in Mumbai are definitely nicer to do business with & although they don't waste time with pleasantries are still gracious, polite & thankful people.
I have some of my best friends in Mumbai available on call 24/7 & who come to Delhi often & still take time out to drop in at my office to say hello, drink beer or just "hang out".
Delhites on the other hand are evil (not all) & are heavy on Name Dropping (I get that, really I do. My dad's been a lawyer for enough decades to know every single politico in Delhi) EVERY ONE KNOWS SOMEONE.
Mumbaiya Guys are cool & don't give a shit who you are or what's your background. They will trust you blindly & open their homes for you.
When I started my Broadband company my first & only investor was from Mumbai, he is an ex-BOA guy who owns more rentals than anyone I know. He insisted in investing in me when noone had any clue what we would do or becvome; not even me.
He saw "Potential" when we everyone all saw "Crazy". He is also pushing me now to complete my book (fiction) which I stopped writing a year ago & publish it for me. He is the best Mentor & Friend I got, my strongest Mumbai connection.
I'm not mentioning RoadRage & Rape's cause the traditional media does a good job of covering those. Please let me know what you think. I request you to not be judgmental or patriotic toward your home state but be rational & think which city has given you more. For me Delhi has given me culture & home but Mumbai has given me my Dream.