Odd that, I've got both a 1750GTV and a 1 series coupe
I'd say give or take the fact that one of them is somewhat challenged in the looks department, they are quite alike in concept. Mines got the 2.0 Diesel lump in it, which doesn't really compare with the Twincam in the 1750 but that's progress for you
You know it's quite interesting to compare too, though for this comparison I'm using my 2000GTV, which is a bit of cheat but...
Performance
Up to about 70 there's nothing in it, past that and the BM would pull away quickly. But if you drive the two back to back the Alfa feels quicker and throttle response is streets ahead.
Economy
Better not go there.....
Handling
The BM is probably one of the best handling cars around these days and it has forty years progress over the Alfa, but STILL the Alfa is more fun with it's LSD and delicate steering. To be fair though if I had to get from A to B quickest the BM would do it. (Bloody hope it should you might say too!)
Ride
Probably not much in it, you feel every little lump of gravel in the tarmac through the runflats on the BM, the 70 profile Tyres on the Alfa smooth all that out, but you really feel big lumps at the back when the live axle lifts and drops.
Space inside
There's plenty of space for two in the Alfa, but people are larger than they used to be in the sixties, so getting in the back is a challenge. The BM is fine for four, but when you park them next to each other it's half as big again so it damn well should be!.
Seat comfort and ergonomics and boring stuff like ventilation and sound systems.
Here's where the real differance in modern cars is, on a cold morning you just climb in the BM, switch the heated seat on, turn on the HRW and the demisters, set the Ipod on random and drive off. You would be half way there by the time you've got the fuel into the carbs on the Alfa and cleared the ice off the inside. Those lovely looking seats in the Mk1 1750 are less lovely when you've sat in for few hours too. The sports seats in the BM are the best I've ever had. There's no point in fitting a sound system in the Alfa, you would never here it over the wind noise or the intake roar (OK I've got no sound proofing and K&N's but....)
Still for a Car basicaly designed nearly fifty years ago, the Alfa 1750 GTV drives pretty damn good! and ..... well like you said is one of the best looking cars on the planet
Edit
crash protection..... BM great.... Alfa just dont...... OK!