A seller may think a PE fund with committed capital is more likely to close than an IS. I disagree.
As a seller, you're dealing with a PE Principal. A PE Principal may promise the world, substantiated by committed capital, but ultimately (s)he needs approval from the IC. In other words, the PE Principal relies on 1 source of capital. If the IC says 'no,' then the PE principal will renegotiate or walk away.
An independent sponsor, on the other hand, has "unlimited" sources of capital. Theoretically, an IS can approach thousands of investors and only needs 1 "yes." A sponsor, especially one with a track record, is much less vulnerable than a PE Principal.