It's two distinct languages, not simply accents or dialects so I would say the difference is probably greater than American/Glasgow dialects.

I have had the same discussion with my boyfriend because he claimed at first that Ukrainian was just more diverse and had more words so it was easier to understand the Russian roots (which is bs in my opinion).

Here is what I think is happening: growing up in Ukraine, you cannot avoid being exposed to the Russian language on TV, around you etc... which you can't say for Ukrainian language in Russia. It just takes a little adaptation period before "getting" it, learning the basic verbs and then understanding is easy. I can say that because I experienced it myself. My first week I was having trouble but very fast something just clicks and it becomes fairly easy to get the jist. It probably helped we started in Kiev where people speak surjik (Russian/Ukrainian mixed dialect) and then moved on to Lviv where our hosts spoke pure Ukrainian. I think native Ukrainian speakers never have that moment so there is this common sentiment Russians are just not trying :(