First let me say that the experience that I have with the TS-590S is playing with it in the store. I don't personally have this rig. That said, there are a few differences that are apparent right away. The first is the price. Configuring the K3 in the manner you've indicated (your filter choices aren't valid, though) is going to cost more than the TS-590S.
The TS-590S is a great "bang for the buck" rig and has a well above average receiver. Take a look at the receiver test comparisons that Sherwood labs has published at
Receiver Test Data. That table is sorted by dynamic range with the best on top. Note the TS-590's dynamic range results compared to the K3 and you'll see a significant difference. There are other differences as well; some more pronounced than others.
In my opinion, the two rigs aren't very similar except for their usage of roofing filters. Even then, the K3 gives you the ability to use more roofing filters or just mix and match to suit your needs. The K3's added expense can be justified by the additional features that come standard. These features include things like 8 band transmit AND receive equalizers and a TX noise gate (that's almost like having a W2IHY stack built in!). The K3's SDR design means that Elecraft is constantly implementing new features and improvements at no additional cost. You also get a rig that is very flexible and can grow with you as your needs change - the options can be added later when you decide you need them.
In summary, they are both good rigs but you'll have to decide what is important to you. I don't think you can go wrong with the TS-590S, but it's not nearly as flexible in the long run.
If you are willing to spend a little more, go with the best-in-class K3 and enjoy a rig that you will have for a very long time, regardless of where your radio interests go.