Great question! Thank you for asking it here on Clarity as I'm sure the healthy discussion will also benefit many members of the community.

I have to admit that my answer will be biased as both of my first two successful startups that I sold ("exited", more here: http://www.linkedin.com/in/exitcoach) had no outside investors, thus my co-founders and I walk away with a HUGE smile on our faces because we had NOT diluted our equity. Why would you want to dilute your equity stake unless there's STRATEGIC reason, right? Raising funds for the sake of raising funds (aka joining the fundraising "frenzy") has a multitude of negative effects, for founders, their employees and even the startup ecosystems. Unfortunately it happens a lot: http://ExitCoach.fyi.to/ExitMess. Perhaps a discussion for another day. :)

Back to your question! The 2 main factors in the "equation" are the investor and the investee (yourself). Ultimately, it's the underlying mindset of both that will be fundamental to a successful outcome.

I believe in using EXTREME examples to understand concepts. Let's say for example that you are a veteran entrepreneur that has built and successfully sold multiple companies. You also have the Wisdom to not be used by the excess cash (the "temptation is REAL, first thing I see after a fundraising announcement is a hiring spree), but put it good use, wisely. And on the other side you have an investor that has all the industry connections, that is a serial entrepreneur as well (has built and successfully sold multiple companies) AND is a "saint" (extremely favourable terms for you), then BY ALL MEANS take the money!! It's a no brainer.

Any other type of "equation", unlike the one above, carries extra additional risk and should be analysed on a case by case scenario. Many startups fail, precisely because they lacked the Wisdom and did not think strategically fundraising. Rather than seeking proper advice, as you already have, they followed the fundraising "frenzy".

I'd be happy to take your call here on Clarity and help you write a beautiful story out of your own successful entrepreneurial journey. Thank you!