I've had my P-07 since 2012 and fired over 5000 rounds through it...
I bought the SP-01 version of the 2nd gun.
The OP is asking for a comparison of the P07 and P01 and your comparison of the P07 v. SP01 (and comparing as carry guns) is a bit unfair. The SP-01 and P01
are not the same gun. The SP-01 is more than 12oz heavier than the P01 (40.7oz vs. 28.1oz), nearly 1" longer (8.15" vs. 7.2"), 3/4" taller in the grip (5.79" vs. 5.03") and almost 1/10" wider (1.46" vs. 1.38"). The SP-01 is a large range gun and definitely not well suited to CCW, the P01 is a compact and a good CCW gun. They do have a similar look though (both are CZ 75 based guns with an accessory rail).
For the OP, I do not have a P07, but I did recently buy a P01 (I have had a CZ 75B for around 15 years and I'm a big CZ fan). I can't give an account as someone who owns both, but I can give you the reasons I picked the P01 over the P07 (and as a teacher, I am definitely budget conscious).
Based upon measurements on the website, they are pretty close, though there are some differences. The weight difference (the P07 is 0.4oz lighter) is pretty marginal and on a good belt will be unnoticeable. The length is the same, and with a canted holster I'm not sure the height difference will be noticeable (the P07 is 0.27" taller). However, when I carry, I find the width of a gun makes a much bigger difference in its concealability than just about any other attribute (I carry IWB) so the 1.38" width of the P01 is definitely an advantage vs. the 1.46" width of the P07, though it wasn't the deciding factor.
When handling them at the gun shop and dry firing them, I found the P01 feels like a slightly smaller version of my beloved CZ 75B (or the 85 Combat a friend used to have). My CZ 75B fits my hands perfectly and I shoot it better than any of my other guns (even when I don't take it to the range for a while, I am always more accurate with it than any of my other guns, even when others have had much more use recently). On the other hand, the P07 doesn't have the same feel (though, this is just dry fire and handling at the shop, I haven't been able to compare them at the range). So, for me the deciding factor was how they felt compared to my CZ 75. The P01 feels like the gun I shoot best (only 1911s can compare) while the P07 feels like a completely different gun.
So, when recently looking at guns in this size class, I bought the P01. For me it was the better choice. However, both are good guns so you should go with whatever speaks to you. As others have said, there are alternatives to the P07 mags if you find them too expensive, and for the price difference between the P01 and P07, you can probably still buy a couple P07 mags so that definitely shouldn't be your deciding factor (though if you were thinking between the P07 vs. something like the Glock or M&P I can see it being a factor).
As for sights, I think the P01 and P07 will use the same sights. I'm pretty sure most of the P07 (other than the modular safety/decocker and the polymer) is based on the 75B series, but the compact and full sized guns do have different height sights.