Yes, the Genesis has the block heel. I know for some that can be a deal breaker.
You may be more likely to get a consistent product from Japan in terms of build quality and fit/finish, which might be something to consider if you're buying without checking it out in person. Though, Premiums have gotten better in recent years. Some people also like the original wild colours but don't care for vines, monkey grips and other Vai-isms, so the Genesis, with the classic looks, hardware and pickups you don't feel bad about changing, is a good compromise. For me, at least, from a $ view and these additional factors, I'd choose a Genesis over a Jem (not dissing Jems, I do like some of them!). I'd get an RFR, chuck a set of PATBs in it and call it a day

.
A Prestige RG can be a somewhat different kettle of fish - if you want something with the option of an ash or mahogany body, 7 strings, different kinds of pups and configs, then yeah, spending 2k is good value.
As for the Genesis being without a case, well, it's not advertised as coming with one and that's one reason they are able to keep the price to 1k. If it came with the usual Team J. Craft job, it would probably cost $1300-1400. Technically, the Genesis is not a Prestige, the latter being marked as having extra work done to the fret ends and fingerboard edges.
The Jem Jr. is basically a mid-tier RG with some of the classic Jem features and looks, and compromises on hardware and pups to keep it around $500. As many of us know, these things – with a bit of a setup and some tweaks – can be very fine players.