Being deeply experienced with both, let me try to sum up the comparisons here. Beaver Builder is ROCK SOLID and this is why many developers choose to use it. Beaver Builder is more stable partially because it improves at a snail's pace in comparison to Elementor and other builders.
Elementor, on the other hand, is crushing all other page builders in the features it has and the value they are adding to the page builder. In 2019 alone they have released many features including a popup builder, motion animation engine, and soon will be adding global styling.
To get the Elementor Pro feature set in Beaver Builder, it would cost $99 for Beaver Builder, $147 for Beaver Themer, and optionally $69 for an add-on package. Where Elementor Pro will cost as little as $49 for 1 website, or $199 for 1,000 websites. However I usually base my decisions on features and not price.
All that being said, both are great builders and it really boils down to what you want and what your needs are. What your priorities are. For me, I want a builder that brings features that I can leverage to improve the user experience on my websites, without having to add any custom code however your situation may be different.
My best advice is to try out the interface for each and figure out what features you need in a builder then make your choice from there.