The 620 uses a two-piece barrel, which I'm going to assume incorporates a sleeve inside a shroud. I'm not fond of the idea.
The 620 is also a seven-shooter. I suppose that's okay, but I'm something of a traditionalist. I'm assuming that the 620 is also an L frame gun, just like the 686, which has also been built in the seven-shot configuration.
The Model 66 K frame has been around for quite some time and has a proven track record. You can often find 66s at gun shows and in pawn shops for about half the MSRP of a new 620. Also, quite a large number of the M66s were built prior to the introduction of the Massachusetts lock in the frame.
Both have adjustable sights. If it's a 66 built before 2000 or so it'll have solid steel hammer and trigger rather than MIM (Metal Injection Molded) parts. Also, the 66 might have a hammer nose firing pin instead of the more recent frame mounted firing pin. Personally I have no particular preference in this, as I've owned both versions, but the only 66 I currently have is a 2 1/2" round butt model built in 1980.
Did I mention that there are going to be several configurations of 66s available, depending on what shops you hit and the phase of the moon?
If you're uncertain, go for the newer gun, as it will incorporate all the available "improvements." According to the S&W website, MSRP on the 620 is $705, but you can expect to pay as much as $125 - $150 less if your stocking dealer is in a good mood. The Model 66 has been around for a very long time, so you might find anything from a 2003 Performance Center gun all the way back to a San Diego County SO marked 4" service weapon.
I bought a 620 last year and it's a really good revolver. That being said, it lacks the character and history of the old Smiths. I've got a blued 19 2 & 1/2 in and a 65 3" that both are classier guns. The 19 is especially nice since it has a pinned barrel and recessed chambers. It was made back when they really knew how to make them.
I haven't any experience with the newer guns as I only buy older Smiths without the internal lock, but for what it is worth, I have personally heard two very knowledgeable gunsmiths (one is an American Handgunner Top 100) disparage the MIM parts (specifically referring to Smith and Wesson revolvers). Also, you can also almost certainly find a very clean 66 or 686 selling for much less than price of the 620 if you look around a bit. Good luck.