If you are looking for visible colour contours and like low colour counts, then there is little to choose between them. Might as well choose the first one you come across.
If, however, you prefer a more accurate representation of the picture with more flexibility of the conversion, colour count, dithering. If you also need to select the floss used or even use blended threads etc, then you would do better to ditch the web based conversions and go to decent software packages. You can get really good conversion software for nothing, so it's not necessarily a costly option. What you need to do, when using software on your computer is to be prepared to demand the best and make sure you try lots of options so you can get the best.
Paid for software, good stuff is 'Pattern Maker' for 80-140 colours. If you have a PC and want to spend nothing, then my software is good for colour counts in the range 80-7000 colours. PC Stitch is paid for software that gives adequate image conversions, better than the web sites I've seen, but much worse than Pattern Maker or my software.
So, decide what quality you want and aim for it. Web sites aim low, and don't always hit their target.
Sorry if my contribution isn't too helpful for you.