Have you got the Users Manuals for the Flukes you mention?
Both are available on line.

I have had a go with the 620. Like all the latest kit, it seems, it's a big lump of "styled" plastic. But it was rugged and functional. I haven't actually had a go with the the 612, but would say that it's probably meant for "mobile" (on site, whatever) use, whilst the 620 is best kept on a cart in the workshop (or on the famous biomed cart)! Both do ECG output as well, of course.
You might want to think about Standards, whilst you're at it (and whether you still want a 25 Amps *capability). Like the 288, both the 612 and 620 can "do" 62353, apparently. I could be wrong, but I don't believe the 277 does. I like the 277. It's a rugged bit of kit (being an evolution of the 255), but getting a bit long in the tooth now, I would have thought (in fact I'm surprised to hear that they still make them)!
Another factor could be ease (or lack of ease) in connecting to output devices (printers, PC's
et al). That, and compatibility with database software. Just like everything else, when it comes to splashing out for new toys, it all depends on what you actually want to
do with them.
The final decision whether to go for one (or both) of these
versus the others you have mentioned may have to be taken on
cost, I should imagine.

Meanwhile, I still haven't tracked down my
medTester. 'Course, then I would need (or at least,
want) all the flippin' modules to go with it!
*
As often stated, I'm a 10-Amp man myself (best stick with the 601-Pro, then).