Well, I have, so I'm biased.
It's not about the number of cc's the engine has. It's about how it delivers power.
I won't get into the gorpy details of torque, horsepower and dyno charts here. Suffice it to say that in the real world of street riding, power and torque down low are better than lots of power at high revs.
A very popular (and now discontinued, sadly) midsized bike is the Suzuki SV650. It makes a lot less power than a 600cc supersport at high revs, but it makes MORE power and MORE torque where it matters, at about 5,000 rpm.
650 is more cc's than 600. But it doesn't matter in the real world.
My bike, a GSX-R750, makes power and torque like the SV at real-world rpms AND also makes huge power when you wind it up. Cool, huh?
If I were moving up, I'd think about the following, in order of priority:
1) Livability. What will the bike be like to live with every day? Will you struggle to back it up the slightest incline? Will it be so tall that putting your foot down on a little gravel will present a real risk of dropping the bike? Will it have such an extreme riding position that you'll want to throw it off a bridge after a few hours? Is it so freakin' heavy that you struggle to get it up off the kickstand? That Daytona is very sexy, but it's a bit tall.
2) Real-world utility. See above re power and torque. A high-strung sportbike that only gets fun when you're screaming around at license-suspension speeds can be frustrating on the street. Look for what it's like to ride at 35-60 mph where you're going to be spending 99.99 percent of your time, not at speeds you're not likely to ever see.
3) Ride quality and handling. Bargain-basement bikes have bargain-basement suspension, wimpy brakes and crappy tires. You can fix all of this, of course, but it's a factor in choice.
4) Bang for the buck. My bike cost four times what I paid for my Ninjette, has five times the performance and costs seven times as much to insure. Make sure you do your homework.
5) Personal preference regarding bike style. I love sportbikes and the sportbike riding position. This stuff matters.
6) Looks. Part of motorcycling is that it moves your soul. It's hard to love a bike you can't stand to look at. But I put this last for a reason... choosing a bike simply because it looks cool puts the cart before the horse.
My own choice of a GSX-R 750 was motivated by the desire to have a true sportbike experience, including the track. If I knew I'd only ride on the street, I'd have gotten something else.
A great choice as a practical, affordable step up:
KTM RC-390. A very sizeable bump in power from your Ninjette, very light, very sporty, very user-friendly, funky style. Ride it right and I'll bet you could keep up with your BF everywhere except the straights.
Upgrading to a midsized true sportbike, I'd go for:
Kawasaki ZX6R 636 (great package with good features, looks sharp)
GSX-R600 or 750 (bias speaking here... but it really is a great bike and good for short people)
Triumph Daytona 675R (sexay)
Current faves in the non-sportbike category are:
Yamaha FZ-07 and FZ-09
Triumph Speed Triple, except for those damned praying-mantis headlights. Ugh.
Ducati Monsters or BMW R-nineT if you've got the coin.