I can't remember how many times I've answered this question - but I reckon my answer is always raw & large fine jpeg. If I've got a very good reason to shoot jpeg only (including reducing the file size/quality) , I will do. If I've got a very good reason to forsake the jpeg and have the raw files only, I will do. Mostly I have no need to make the choice before the shot so I don't. Sometimes the camera jpeg suits my needs, sometimes it doesn't - I tend to make the choice after the shoot.
I don't relish hours of PC pp (I don't get enough time and opportunity to get out with the camera, let alone work on the captures) but I'll gladly do it to get the end result that I want. I'm a 'for pleasure' photographer with no one expecting or relying on a professional product so I can stick a thumb in both pies and then choose whichever I want or just leave them and move on to the next two pies - it's not always a big deal to me and 99 times out of 100 I will work on a raw file to get the result I want but I don't always have a high bar to reach and I do like to have the easier (and often quite adequate) option available

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If you feel that you're not improving on the camera jpeg when working on your raw files then I dare say that you're not alone but it will take time and practice to start to get the result you want. I often find that the more I work on a raw file, the less satisfied I get with anything to do with the picture - but I show a few versions to my partner and she immediately points out the pros and cons of each effort (though she wouldn't know what a blown highlight or white-balance is, she can still see and appreciate the differences between the versions).
Imho, if you identify and practise a few basic steps to put in to your raw work-flow, you will start to feel more useful with raw pp and to enjoy the freedom and the determination/control that you have in getting to the end result.
I would suggest that some basic steps to consider are white-balance, colour balance/saturation, brightness/contrast (and get to play with levels/curves) and sharpening.
Here's a
beginners guide to RAW
and
here there are loads of guides for getting specific techniques right in pp
EDIT ps: I have no experience of Photoshop Elements and haven't a clue as to what it is or isn't capable of.