Money: Deep, deep pockets have to be at the top of any major label "pros" list. Even with major-label music sales declining and the industry as a whole struggling to keep up with changes in the way people purchase and listen to music, major labels still have a huge financial advantage over just about every indie label. When your label has a lot of money, that means they'll be able to spend a lot of money promoting your record - which is exactly what you want. It also means they may be able to offer you a large advance and invest a lot in recording, touring, video shoots and other opportunities for you.
Connections: Money helps open a lot of doors, and when a major label comes knocking, most media outlets are ready to let them in. Additionally, most major labels have been in the business for decades and have long established connections that help you reach your music career goals.
Size: Alas, size CAN matter when it comes to record labels. Major labels are behind the vast majority of music sold, and this scale of operations can bring many advantages. First, they can get the best deals on manufacturing, advertising, and other expenses since they do business in such enormous bulk (they have way more purchasing power than indie labels). Second, because of all of the artists on their roster, they can pull some pretty big strings in the media. Here's a VERY common scenario: a major label may call up a big music magazine and say, "hey, if you want to interview (insert mega-selling artist), we suggest you review/feature (insert brand new, unknown label signing)." This is great for you, if you're that new label signing, because you get instant press in all of the top spots, giving you maximum exposure overnight.
Big Pond, Small Fish: A lot of major labels tend to sign a lot of musicians and throw out a lot of music, just to see what will stick. As a new signing, except in very special circumstances, you're likely to find yourself fighting for attention from the label. If your music doesn't start sticking - read: selling - pronto - then you can find yourself with a record out that isn't getting much promotion and a label that doesn't return your phone calls.
Continuity: A big part of avoiding the aforementioned "big pond, small fish" syndrome is having a big fan at the label. Usually, this is the person who signed you. However, turn over at a major label can be pretty high - especially in this day and age - and you run a high risk of waking up one day to find out that the person who loved your music is no longer working at the label. The new person who takes over your album may not be such a big fan, and suddenly, no one is too interested in making your album a priority. You can include a "key man" clause in your contract to try to avoid this, but often the bargaining power is against you when you sign a major label deal, so scoring this set up is not guaranteed.
Artist Unfriendly Deals: Not every major label deal is unfriendly to the artist, but many of them are set up so that if a cashier accidentally gives you an extra dollar in change, you have to pay the label 50 cents. OK, that's an exaggeration, but many major labels want to sign artist for multi-album deals that offer them very little flexibility and that hand over a lot of creative control to the label. They know all of the loopholes, they want a piece of everything, and they have better lawyers than you.
The Passion Question: Many dedicated music lovers work on the major label side of the music industry. However, not everyone who works at major labels loves music. You'll find a higher concentration of people who are in the business strictly for the money in major labels than you will at indie labels, and that often ends up rubbing musicians the wrong way.