HI Mike,
I listened to a bit of both tracks. I think both have good vocal recording quality if you look at that in isolation. I wonder, though, what the specific adverse comments were. For example, on the first track, "One Time", it struck me that the quality of the vocal was quite good, but I'm not sure it fit the relatively modern style of the track. It felt like it was a more vintage thing, maybe kind of around the era of Mike & the Mechanics, for example. The other, "Can't Stop Myself", maybe was a bit more uneven on levels and confidence, but, overall, I still thought it was pretty good. Here again, though, I was hearing pretty modern production techniques, for example on the drums with the machine-gun-style hits, but the vocal felt less modern, or maybe just a different musical style. Just as one thing that comes to mind, a lot of the pop vocals tend to feature fairly heavy tuning effects, which these did not have. If you're hiring others to produce your vocals, you may want to be sure they have the reference tracks to compare for any production style considerations. Of course, the singing style would have to match, too, and that can sometimes be a consideration if, for example, the style needed simply isn't one that is all that compatible with your own singing style.
To more directly respond to your question, though, getting the hang of producing our own vocals can be challenging, and there are a whole bunch of things that enter into it. In my case, I've been singing "forever", but I am most comfortable singing while playing piano (or other keyboards). Tracking vocals while standing at a mic in my home studio was, and still is to a degree, way less comfortable. Also, there is a lot of leeway in live performance since people hear it once, see the performance, too, and might even not be paying all that close attention in a bar or club. Whereas a recording is something that can be heard over and over, so flaws tend to stand out.
Beyond the comfort factor consideration, the first issue I had, after "upgrading" from an SM58, which I've long used for live performances, to a condenser was that the mic really wasn't a good match for my voice. It seemed to highlight the not-so-great things instead of the more interesting things, though it sounded great on a few female vocalists I recorded with it. I found that Antares Mic Modeler let me, at least in theory, subtract the characteristics of my mic and add on the characteristics of various other mics. I'd never used most of those mics, so I can't vouch for any accuracy, but what I found was when I used Mic Modeler to simulate a Neumann U-87, all of a sudden my vocals were much improved on the tonal front. I've since bought another mic that is inexpensive, but had been heralded by some engineers I respect as being U-87-like. That one ended up being a much better fit for my voice.
The second issue I had was intonation. While my intonation is generally good enough for live, it really wasn't good enough when standing at a mic overdubbing vocals in a studio. So I was having to pay more attention to staying in tune than the emotion behind a vocal, which made for a tradeoff between emotion and intonation. Once I started using AutoTune in graphic mode, I could focus more on the emotion of the performance, a long as the tuning was close enough to tweak later. I've since shifted to using Celemony's Melodyne, which ends up being a lot easier to use, and with fewer artifacts than I was getting with Autotune, but the bottom line is still similar -- I can mostly go for the performance, not worrying as much about intonation.
Mic technique is another consideration -- things like moving in and out to deal with volume considerations, whether you want proximity effect or not, etc. That's really not all that different than singing into a mic on the live front, though, so that has been more natural for me.
Beyond that there is the whole processing thing, and trying to make it fit in the track, fit the genre of the song, and so on. I guess that is mostly a matter of trying to figure out what is going on in the genre you are producing at any given time. I certainly won't claim to be any expert on that stuff, though most of the time my stuff seems to do okay on the vocal front, with only a few rejections mentioning vocals, and mostly in the context of not being right for the specific genre or vintage.
I'm not sure that helps very much, and, of course, I suppose it is a matter of taste a to whether I've actually learned to record my vocals well.
Rick