Pros at Fidelity:
If you have a lot of customer service needs, you will almost certainly get better service. You don't wait on hold as long, they're more likely to do things correct the first time.
Expenses on their index products and other ETFs available through them are on par or even cheaper than Vanguard products right now.
Cons at Fidelity:
Fidelity's structure is such that they prefer to push clients into high-expense active funds. If you're an experienced Boglehead, it's not particularly difficult to avoid these. However I think of my parents, kids, siblings, etc who aren't as financially inclined. If I encourage any of them to open an account at Fidelity, I would not be surprised if they fell victim to an expensive asset management service with high-expense funds.
That high service you receive from Fidelity doesn't come from nowhere, someone is paying for it. And if you are investing only in low-expense ETFs and Vanguard products, you are likely costing Fidelity much more in customer service than you are paying in any kind of fees to them. Your higher level of service is being paid for by other customers who fall for those high-fee traps and are paying through the nose. Is it sustainable long-term that Fidelity would do nothing about some of its clients being a net cost to them? Fidelity is a private company owned by the Johnson family and those owners want to see a profit. Could they target the clients who are costing them money at some point in the future? Maybe.
While Fidelity funds have lowered their expense ratios to be competitive with Vanguard, this is almost certainly a loss leader for them. It is very unlikely they are making much if any profit on these funds. They also are much less likely to share their security lending revenue with their shareholders, and this can easily be worth between 5-25bps. I worry about buying a bunch of a fund in a taxable account, building up huge capital gains, and then the fund expenses increase significantly. Then I'm stuck in a high-expense fund that I can't sell without massive tax consequences. This could happen at any fund family, but I feel that Fidelity's corporate structure incentivizes it.
Pros at Vanguard:
If your customer service needs are minimal, their service as perfectly adequate. If you're the kind of investor that invests in 4 funds or less, Dollar-cost-average in, and just invest in simple accounts (Individual, Joint, Trad IRA, Roth IRA), and prefer to do everything on the web anyway, you'll almost certainly be perfectly satisfied.
Expenses on Vanguard products are nearly always either the lowest or very close to the lowest in the industry. They also share more than 90% of their security lending revenue with their shareholders, which at 5-25bps can make a much bigger difference than a 1-2bp difference in expense ratio.
At Vanguard, I know that I can help my friends, family, etc open accounts and know that they will never be taken advantage of. They will never be put into high-expense ratio funds, or be enrolled in a high-cost advisory service. The only advisory service Vanguard offers is at a cost of 30bps and honestly is probably a pretty great value for anyone who doesn't have the time, ability or willingness to manage their own assets (A large majority of Americans). I can rest easy knowing that if I pass Vanguard won't tell my heirs to sell all my index funds and put everything into this fancy new actively managed fund that will make all their dreams come true.
Vanguard's corporate structure is set so that expenses should be pushed lower over time. Vanguard's stated mission includes lowering costs for all investors (and in fact is a very large reason behind why companies like Fidelity even offer low-expense funds). It is very unlikely that the expenses in my Vanguard funds will jump up significantly, or that Vanguard would ever decide to move away from index funds as a corporate strategy. I can invest in Vanguard funds in a taxable account with the comfort of knowing I won't get stuck in a high-expense fund at some point down the road.
Cons at Vanguard:
If you have a lot of customer service needs, Vanguard is not currently great at that. The hold to talk to a rep is usually pretty long, and it would seem many (if not a majority) have pretty low tenure. If you have complex account types (SEPs, SIMPLEs, solo 401ks, 403b7s, trust accounts, organization accounts), their web interface can be frustrating. If you are looking to trade a lot of stocks/ETFs/etc you will find Vanguard's brokerage platform to be somewhat Spartan. If you like to have physical offices to walk into, you won't have that with Vanguard.
In the end, it depends on what type of investor you are. Many, if not most, Bogleheads like to keep things as simple as possible and for them Vanguard is more than sufficient to meet their needs. Others have very complex needs and hate to use the web, so would much rather take their paperwork to a physical office and have someone help them fill out every page while sitting next to them.