I find that with RT the default settings do indeed look a little bit less like my camera JPG than they would in, say, Lightroom, not that this is necessarily a bad thing, but they do. When I tried RT I was convinced it was capable of better results, but I knew I would need practice, so I kept Lightroom for a few more months, and I would practice with photos I’d done already in Lightroom, or process a new photo in LR and then try it in RT. A lot of the time, RT was better, but not every time, or it would be better in one way but worse in another, so I’d go back and play with it and try to figure out what I did wrong. I did this as a kind of hobby for several months, and eventually deleted Lightroom. The point is, there’s a learning curve, and, while I love to rag on Adobe as much as anybody else on the internet, it might indeed be helpful, as you suggested, to download the trial and do some practice with both, comparing results and adjusting your technique until you can get something you’re happy with in RT. Alternately, try RT on some photos you’ve already done in Lightroom and see if you can figure out where you’re going wrong without installing it again, although this might require more intuition and trial and error. Output from the two shouldn’t be identical anyway, but they’re both reasonably powerful (RT much more so I would argue) and either should be able to produce a half decent raw conversion. Had I made the switch immediately, I might have struggled more, but I was able to figure out how to get results that are reasonably similar out of each, just usually RT would have a slight edge in detail. If the colour didn’t match, I’d go back and season to taste.
I’m not sure how specifically to make your photos look better to you, but I will say that I find that the curves are a much bigger part of my workflow in RT than in LR, I find that a big part of the way a picture looks (including how “strong” the colour are) when I process it in RT is achieved in the curves, a lot of the other tools get used more sparingly. Try flattening the default curve and playing with it yourself, play curve one against curve two, and experiment with the different modes for them to see how they effect colour. I would often skip curves in LR, or use them to a much slighter effect. In RT, since there are 2 (plus 9000 others sprinkled throughout the program), and because of the way they work, I find they’re a much bigger part of how I get a picture to look how I want than they were for me in LR, I can spend a fair bit of time and consideration working on the curve of a photo, everything else can usually be done pretty quick and business like for me.
As far as removing a cast, the color toning tool can probably help, but I find the a and b curves in the lab controls the best way to remove (or add, if I want to) a cast to a picture. The various LAB curves are the way I prefer to adjust the way colours look, although there are numerous ways of doing this in RT. BTW I tried ART recently and really liked it, but kind of missed all those LAB curves, so for now I’m sticking with RT.
I think you have a lot more control with RT and its more powerful, although I probably spend more time per photo now than I did using LR. More experience might help my efficiency, but having more tools and (I think) more power and control, it might be unavoidable that you can end up spending more time.
I don’t know what kind of camera you use, but I was able to take some DCPs from Adobe DNG converter so I’m able to apply “camera landscape,” “portrait,” etc. to get a different starting point with certain Canon cameras. If Adobe has the DCPs, and you have the camera, you can apply them in RT. This gives me a little selection for different colour interpretations to start out with, but I don’t think it saves me a great deal of actual time, I still have to fiddle with the curve on a per-photo or per-batch basis. You might be able to find a curve, DCP, film simulation, or other kind of “preset” to get you where you want to start out from (or make one), but my experience is you really have to put a little bit more thought and input into each photo (or batch) in RT than you do with LR, but for me, its definitely worth it.
I hope you can achieve the look you want, I’m just a user but I love to evangelize RT and hope everybody can enjoy it at least as much as I do, but I understand it can be frustrating if you’re not getting results you’re happy with. This was my experience with darktable, its obviously really powerful and I’m sure great results are possible, but I wasn’t able to figure out how to get them myself. Of course I didn’t spend several months using it parallel with LR and comparing results like I did with RT (not to mention dt has been massively updated since I last tried it), so I suppose that’s understandable.