I have a couple other important considerations regarding external HSA accounts vs employer sponsored HSA accounts.
Depending on your personal financial situation and goals; some people like to use HSA accounts as an extra retirement account (since the money can be withdrawn penalty free in retirement for non-medical expenses, and completely tax & penalty free at any time for medical expenses). If your intended use for the HSA account is an investment vehicle for retirement, then you may find more use/benefit out of an external provider that may provide more or better investment options than your employers HSA investment options. There can be a lot of additional value in those extra investment options over greater periods of time.
Another VERY important consideration for FICA taxes (FICA includes Social Security & Medicare) that I don't believe was mentioned before - for those earners who are under the maximum social security wage limit, you are paying 6.2% of each paycheck into social security taxes. As others have mentioned you can "save" this tax through your employer’s plan if you set up the account to be funded pre-tax from your paychecks. However, in doing so, you are lowering your overall contributions into social security, which may lower your social security benefits in your retirement years!
If this is ultimately going to lower your SSA benefits in retirement then that is a big future cost that may steer you against the pre-tax employer contributions. Think of social security as part of your retirement plan, not as a tax but instead as an additional check you put away for yourself for retirement every month. Of course, this is only an important consideration if SSA is still going to be around when you retire, but let's assume that it will be.
This is not an issue for higher earners, earning well above the max SSA taxable wages. There is no wage limit on the 1.45% Medicare tax withholding's, and there is certainly no harm in saving Medicare taxes because it will not affect future Medicare benefits. So for taxpayers earning well over the max SSA wages, they will just save the 1.45% Medicare taxes without affecting their SSA contributions and resulting retirement benefits.
So again, it all comes down to personal situations. Depending on your earnings and goals, employer plan may or may not be the way to go.
Personally, for my lower earning clients, friends and family, I tend to recommend that they do whatever they can to maximize their social security benefits in retirement. So I would advise them to either use the external provider account, or the employer plan but with post-tax contributions so you don't lower the SSA withholding's but can still claim the income tax deduction on your tax return.