Question: Is there any distinction between 二倍 and 两倍?
It actually comes down to situational preference and the distinction is marginal at best.
Other contributors have already made some pointers.
However, I just wish to add that:-
(1) when making a general dimensional comparison, 两倍 is preferred; such as 两倍大, (twice as big), and 两倍多, (more than double)
(2) Also 两 is preferred when it involves an approximation without quantification when things are figuratively "doubled", like, 他眼睛比我的大两倍, (his eyes are twice as big as mine)
(3) 二倍 is preferred when some quantifiable comparison is made, like, 今天的收入涨幅了二倍，(today's income increased by two times) because 倍 by itself means "times" as in "how many times" something has increased by.
But, in most cases, the two words are interchangeable and any distinction could be a matter of preference.