By all means - enter away.
But don't be surprised if it comes back as alreday owned and a re-roll will have to be made.

Why would you enter, if you own the newer version of the same game?

Weird, that last post was cut off at the end, looks like it glitched while I was posting it. I tried editing it to have a more conclusive end, now. Fixed some confused parts in the first post, as well. Sorry about that.

And yeah, Legendary's still a completely worthwhile version of the game. Again, it's down to those comparison videos I posted above, and down to which mods you prefer. If all you're going to be using is graphical/convenience mods, and you don't care about having it absolutely perfect, LE'll be fairly identical as an experience, and will still provide a comparable content mod experience (especially as many of the notable newer SE-exclusive mods.seem to be paid content club offerings, so if you don't want to pay extra for mods, you may perhaps not really be seeing any new mods you want with SE to begin with).

Thereby, if you're fine with the basic verison of Skyrim, then Legendary's probably going to be just as good for you as SE would be, and it's definitely the best option for you getting your missing DLCs for the basic version.

SE's no longer as bad as it used to be but, conversely, it's not near as much of an improvement over Legendary as others believe it to be. Again, it's mostly going to be down to subjective preference on the graphics if you're not using mods, and down to which content mods you prefer. Of course, if you want the best graphical experience, you'll want to go SE with full graphical mods, but it's not like LE doesn't look great after graphical mods as well. Personally, I'm okay with either version of the game, so I imagine there'll be others who will be as well.

As far as the stability aspect, SE is built to run at 64 bit (which does mean it likely won't be able to run on older OSes, given that I can't find anything about it having a compatibility mode), which lets it do things like utilize more memory and process larger calculations. Generally speaking, from what I've seen and understand, this'll mean things like improving distance rendering, smoother area transitions, and so forth. It's stuff you'll appreciate once you have it, but not stuff you'll realize you're missing until then. It's kind of like upping frame rate on certain games that already have a passably smooth- but not excellent- frame rate to begin with.

More notably, while SE apparently has some new internal stability issues (ie, new CTD inducing bugs and a higher tendency towards generalized bugs) this increase in its available memory usage also means that it tends to manage excessive amounts of mods much better than classic Skyrim did. So if you're planning on loading the game up with an exhaustive amount of mods, SE may actually be a better option for that reason alone.

Though, as I noted before, SE and LE have somewhat different modding environments. So, from a stability perspective, LE could actually be a better (or at least equivalent) option for those who don't intend to do much content modding. SE, on the other hand, would be favorable for those intending to load up dozens, or even hundreds of mods at a time.

I'm not good at extrapolating what people are needing, a lot of the time, so I do tend to give verbose answers to try and cover the bases. Sorry for the length, and hopefully I covered what you needed. :)