On my calibrated screen both your photos look fine to me but as peakoverload has said your imac screen will be very bright which will make your images "pop" out of the screen. But this is an artificial brightness which won't be replicated by the printer at Photobox.
So it sounds like you need to calibrate your screen. I had the same problem with prints from Photobox coming back alot darker than on my PC laptop screen. I bought a Spyder2Express from a US seller on ebay and calibrated my screen - I was amazed at the difference once I'd calibrated the screen. Now my prints from Photobox are much closer to what they look like on the screen - it's not 100% the same but it's close enough.
One thing you should try even if you decide not to buy a calibration tool like a Spyder is ask Photobox to send you a calibration print. They will send you one FOC if you ask them and when it arrives compare it to what it looks like
on your screen here. I suspect that the image will look much brighter on your screen than on the print.
One other thing, my Spyder corrected a bad colour cast on my monitor. I didn't notice this but my screen was very blue; I b&w processed about 300 photos in Lightroom for my college photography course and was shocked when they were printed out how brown they all looked. This was because my screen was overly blue. The Spyder has corrected this so the colour is spot on now.
HTH.
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