THE 6D IS QUITE TEMPTING but so expensive
The 6D is quite good for what it is, although it lacks some things a more general high end camera like the 5d3 does well (specifically the AF system and a few edge features). What lenses do you have now? If you have a couple of good lenses, you may gain more by the 6D which will be a big jump over the 500D's sensor in many situations. If you don't have any good lenses, go for a good lens or two, and a good tripod if you don't have one. Don't forget to get a shutter release cable and learn how to use it and mirror lockup for your landscapes.
Ok, so none of your current lenses will work on the 6D, since those are EF-S lenses. If you go for the 6D kit with 24-105L it's a pretty nice all-around lens, but even stopped down it won't excel at landscapes. Great general purpose lens though.
If you're serious about landscapes, I'd first get a good quality tripod. Skip the $200-300 range, and go a bit higher. I don't have the link handy, but basically it's a cost comparison showing someone starting off with a really cheap tripod, decide they need a better one and get a mid-range, then decide they need a better one and get a higher end tripod. In the end, they would have saved money if they had gone right for the higher end tripod. Not that I'm saying you should spend $600 on the lens, and another $400 on the head, but if you can budget $600-700 for legs + nice head, you'll be a lot happier for a long time.
Next, I'd go for another lens. Depends on you're budget and desire, but for landscape I'd go more for the 17-40L or 24mm Samyang/Rokinon lens. That one is manual focus, manual aperture, and you won't have any lens EXIF info, but it is pretty good optically, especially when stopped down to f/4 or a bit further. However, the Canon 17-40L is more flexible, although it starts at f/4 it does improve stopped down and has AF and full lens EXIF info. Both of those are around $600-700 I believe. For you, I'd recommend the Canon 17-40L for now, and it should suit you're needs pretty good.
So, for less than the cost of a 6D body only, you can get a very good tripod and a good quality lens that will be quite good for your current needs, and give you some room to grow and experiment and learn. I also recommend going online and searching and reading about landscape photography. There is a lot of material out there on the internet. I likely will take some time to learn the techniques, and then figure your style, but keep at it and don't give up.