I've never ridden the Monster 620, but I have ridden the M900 and SV650S. The SV is an absolute blast to ride, and it is much more versatile than just a beginner's bike. It serves that purpose admirably well, but the beauty of the Suzook as your first bike is that you absolutely will NOT outgrow it anytime soon. Sure, you may decide to upgrade, but it won't be because the SV just doesn't cut it anymore. Not only do they perform admirably well out of the box, but there are plenty of upgrades to be had, too.
The monster, on the other hand, is a Ducati. This means that while it looks great, it will cost you an arm and a leg in service costs. Without looking at specs, I assume that it is still a Desmo engine, which means lengthy and expensive valve adjustments at very short intervals. That aside, I know that the motor is likely to last a very long time. My friend's M900 saw upwards of 30,000 miles in its first year or so, and it is still running strong. It did need a new clutch, but he rides it pretty hard. I'd bet that parts for the Suzuki are a fair bit cheaper than parts on the Duc, too.
I am under the impression (again, without looking at specs) that the 650 makes more power than the Monster. I know that the 650 can be tuned up to provide many more horses than it comes with, too. Most clubs have lightweight twins race classes that race almost nothing besides SVs, and I've seen some for sale that claim in excess of 90bhp. If that doesn't convince you that the bike will grow with you, nothing will. I can't speak to the tunability of the Duc, but I doubt the aftermarket is getting that kind of power, if only because the thing is air cooled.
Living in similar price points, you can probably assume that they are similarly spec'd in the braking and suspension department. I imagine that either bike will need suspension work as you start to push its performance envelope. Other than that, I imagine that you'll have a blast riding either one.
Something to take into account is the theft rates for each bike in NYC. The Ducati name may hold a lot of allure for a thief, but I bet there are more SV owners out there shopping for cheap parts. Check with your insurance agent to find out for sure.
One other factor to consider, and one to which I cannot speak, is how well each bike holds up to inclement weather if you park the thing outside, ever. My buddy's Monster certainly shows the effects of outdoor parking, even in sunny california. There's a fair amount of fuzzy oxidation growing on many or all of the bolts. I wouldn't be surprised to hear that the Suzuki fares much the same, given their build quality reputation on other bikes.
Most importantly, however, welcome to the fold. You'll have a ton of fun on either bike, and don't be surprised when your recently acquired new hobby completely takes over your life, and even worse...your bank account.
My vote goes to the Suzuki. At least on paper, it seems the better deal, and I know that they are an absolute hoot to spend time on the back of. On the other hand, the M900 was a phenomenally easy bike to ride, and assuming that that trait made it into the littlest member of the Monster family, it could be a great platform for really polishing up your riding skills through that most important first year on a bike. It's probably a bit more comfy and easy to ride in traffic than the SV650s, due to the slightly more upright seating position.
--sam