Are phone app spectrum analyzers accurate?

I'm constantly amazed at the cool things a smart phone can do.  There are several spec. analyzer apps available but I'm wondering if they're really accurate enough to use for system tuning?  I've tried a couple of these and I like Speedy Spectrum and Spectrum Analyze (for android) the best for features and apparent accuracy.
My old Heathkit portable analyzer looks to be toast (yeah--I'm that old).

What are the thoughts from the hive?