Terrestrial radio pays roughly 28% more to publishers per play, per listener than Pandora, according to Billboard estimates from numbers provided in blog posts by David Lowery and Jay Frank. But publishing is a small part of Pandora's royalties. When payments TO all parties (publishers, record labels, performing artists) are taken into account, Pandora's per-play, per-listener royalty is over 14 times that of terrestrial radio.
Lowery's blog post about BMI royalties from radio and Pandora for his song "Low" has gained incredible attention (and 145 comments to date) for its detail and criticism (of Pandora's efforts to reduce what it pays publishers, labels and artists). Frank's follow-up post at his FutureHit.DNA blog includes audience data from Mediabase that allows for an apples-to-apples comparison.
"Low" received $6,888.90 for 18,797 terrestrial radio plays and $84.45 for 1.159 million Pandora plays. (Both figures cover total payments to BMI. Lowery has a 40% writer's share. I assume the publisher takes a 50% share of royalties.) Since many people hear terrestrial radio plays but -- most likely -- only one person hears a Pandora play, it's difficult to compare $6,888.90 and $84.45.
Frank's post adds information about the audience size for "Low." According to Mediabase, "Low" had an audience per play of 3,364 the week ending June 24th and 3,896 the week before that. I used an average (3,630) of these two weeks in my calculations.
At an average audience of 3,630 people, "Low" generated a per-listener, per-play royalty of 0.0073 cents from Pandora -- 27.6% lower than radio's 0.0101-cent royalty.
The numbers for "Low" should not be seen as the rule for Pandora and radio royalties. As Frank notes, songwriter payments "differ drastically" by performing rights organization and by song title. "However," he writes, "we can infer that songwriters across the board are receiving less per impression on Pandora."
Of course, publishing royalties (which Pandora pays to performance rights organizations like BMI) account for about 4% of Pandora's revenues and are dwarfed by royalties paid to SoundExchange for the performance of sound recordings. And radio does not pay for the performance of sound recordings. As a result, Pandora's all-in per listener, per-stream royalty is much higher than that of radio.
I calculated Pandora's all-in royalty by adding its 0.0073-cent publishing royalty to a sound recording royalty that takes into account its business model. Pandora pays statutory rates of 0.12 cents for ad-supported streams and 0.22 cents for subscription streams. Pandora's total revenue is split 83.8% for advertising revenue accounts and 16.2% for subscription revenue. Assuming royalties have the same split, the average royalty Pandora pays for sound recordings is 0.136 cents.
Thus, Pandora's all-in royalty is 0.144 cents (still using the "Low" numbers), 13.3 times greater than radio's all-in royalty of 0.0101 cents.
Radio would incur an immense royalty bill if it had to pay for the performance of sound recordings. The amount stations would owe would depend on the settlement between labels and stations. One estimate is $2.5 billion per year http://davidtouve.com/2012/11/19/2-5-billion-the-big-numbers-that-big-radio-could-owe-each-year-if-it-paid-music-royalties-at-pandoras-rates/ if radio stations were treated like a statutory webcaster and paid last year's royalty of 0.11 cents per play per listener.  
I'll leave it to readers to decide what is a fair royalty for either publishing or recorded music. But the disparity in the numbers makes it clear why record labels are pushing so hard for a performance right.