Some of the difference was due to the different carts, but a lot of it was due to the RP3 being a better deck. I'm not the biggest fan of Rega's carts, but for the price of it with the deck it's a no-brainer. Others love them though. It's all preference, like everything else in this hobby.
Congrats again on the deck. It's pretty much impossible to go wrong with a Rega IMO. Not trying to get you to upgrade or spend more money before you've even got the deck, but you really should look into the TTPSU down the road. It's a very big difference. I haven't heard the RP series, but the P3 with TTPSU sounded better than the P5 without one, when both had the same cart connected to the same system. The P3/TTPSU combo sounded a decent bet better IMO. The P5 with TTPSU sounded far better, but it was also about twice the price.
Just some observations. I'm sure you'll be blown away by the bare RP3 and think I'm crazy. I spent way too much time hanging out at a great Rega/Naim/Linn dealer where I used to live. The owners used to let me hang out and listen to music with them. Had I had more money, I'd have bought everything in sight.