In Hungary, Bela Lugosi had been an established dramatic actor. He did Shakespeare. He played heroes, romantic leads, and all sorts of other roles. In the United States, he made horror movies. Lots and lots of horror movies. He wasn’t happy about that. You can’t really blame him. He did speak fluent English, though his accent was definitely thick, and he could have been in different kinds of movies if there had been more choices given to him.
He was one of the earlier of the “left Europe because of politics” types between the wars. He was actually a socialist and fled Hungary shortly after it stopped being the Austro-Hungarian Empire. He’d done a little acting before the war; he did a little movie acting after it. In fact, the specific reason he left Hungary was that he’d formed an actors’ union. He spent some time in Weimar Germany before making his way to the US in the merchant marines, which landed him in New Orleans.
He’d actually been in a stage show of Dracula well before appearing in the movie and had to lobby to keep his role. He’d finally made his way to Hollywood with a touring company of the stage show and stuck around in the hopes that he’d be cast. He was in a few movie roles. Eventually, he was able to convince them to give him the role, and it was a remarkable success. Arguably too much of a success, if you think about it, as it made it hard for him to find success outside horror. He actually fought as much to get out of horror as he’d fought to get the role of Dracula in the first place.
How did he get along with Boris Karloff? It appears to depend who you asked and when. There’s conflicting reports even in the same place. It’s worth noting, of course, that the script of Frankenstein that Lugosi turned down was not the script that ended up getting filmed; the original script had the Creature even more monosyllabic and bestial than the version James Whale ended up making with Karloff in the lead. However, it is true that Karloff always got billing over Lugosi, regardless of size of the role. You figure, if nothing else, he was frustrated by that.
Honestly, I assume that Lugosi was frustrated by everyone who took roles as interesting Eastern European types who was in fact from England or somewhere. Basil Rathbone actually got a movie role that Lugosi had played on the stage, as Commissar Dimitri Gorotchenko in Tovarich. Still, it wasn’t those frustrations that led him to his dependence on morphine; it was wounds sustained in World War I. Which is apparently what led to his sciatica. He was treated with opiates, and that led to dependence, one of many things which led to his declining career. Still, these days, he’s more popular than Karloff, so that’s something.