I had an E87 130i for 9 years, and last year I replaced it with an F20 125i, so I was in exactly your position!
To be honest, the 125i feels, if anything, faster in everyday driving than the 130i did - it has much more torque at low revs, so there is much less need to drop gears and floor it to overtake other cars. The 130i only really felt fast to me once you'd got the revs up to 4000 or so; the 125i feels fast when you put your foot down at 1500rpm. There's no turbo lag at all that I've noticed on it - it just goes when you push the pedal. I don't know if the one you are looking at is auto or manual - mine is an auto, and the auto box suits the engine very well. Bear in mind there is a fairly big difference between how it feels in Sport and Comfort modes (and in Eco mode, where it feels like the boot is full of cement) but in Sport mode, it feels very nippy indeed.
Handling-wise, there's not much in it - the 125i is a bit lighter, but not such that I can tell much of a difference in terms of how it handles.
I was a bit worried going from the 6 pot to a nominally slower 4 pot, and I didn't get the chance to drive a 125i before I bought mine, as no-one seems to keep them as a demonstrator, but there really is nothing to choose between the E87 130i and the F20 125i in terms of real-world driving speed; on paper the 130i is very slightly faster but the 125i feels just as, if not more, quick to drive. I've got no complaints at all about mine coming from the 130i. I get about 5-6 mpg more out of the 125i than I did the 130i, FWIW.