My understanding is that when characters were being simplified in Mainland China, they first had to standardize traditional characters (i.e. What should these new characters be simplified from?). 「綫」 was chosen as the traditional standard, thus in the PRC's Table of General Standard Chinese Characters (通用規範漢字表), you can see that 「线」 is considered to be simplified from 「綫」, while 「線」 is listed as a variant of 「綫」 (「缐」 also exists, but is only used as a surname).
Understandably, if the dictionaries you are using are Mainland Chinese, 「綫」 will be treated as the standard character rather than 「線」.
In contrast, every other region in the Sinosphere that has some standard for Chinese characters (i.e. Hong Kong, Taiwan, Japan, South Korea) list 「線」 as the standard form, which might explain why 「線」 is much more prominent outside of simplified Chinese.
However, as mentioned in the other answer, 「綫」 is quite common in Hong Kong, despite 「線」 being the standard character in Hong Kong's List of Graphemes of Commonly-Used Chinese Characters (常用字字形表). This is likely because the standardized character shapes are used as general guidelines for education, rather than used as a strict set of rules to follow.
The smaller character here indicates a variant form.
Both these forms have existed as variants of each other for quite some time before the modern era, so aside from regional standards and popularity, one isn't necessarily more correct than the other. I'm not sure about Japan and Korea, but in Chinese-speaking regions, both forms should be equally well-understood. In the end, it boils down to personal preference.