Gothic and Romantic literature both developed at about the same time, the mid-to-late eighteenth century, and both share some similar themes.
Both Gothic and Romantic literature often feature death or suffering as a prominent theme, as well as women as victims. Both often focus on an individual. Both often include elements of the extraordinary or the supernatural, and both, in terms of style, can put great emphasis on describing setting.
A novel such as Mary Shelley's Frankenstein emphasizes the extraordinary. In her case, the story does not quite cross over into the supernatural, but the creation of a living creature out of dead body parts is beyond the reach of real science.
The novel shows both Gothic and Romantic elements overlapping when Victor is shut up alone in his laboratory. The Gothic elements include the creepy experiment he is engaged in, the dehumanizing toll it takes on his health and psyche, and the monster that emerges from his efforts. Romantic elements include the individualism and idealism of the lone hero embarking on an almost impossible quest.
The novel also shows the overlap of the Romantic and the Gothic in women suffering and dying. The Gothic when the women, such as Victor's newlywed wife Elizabeth, an idealized, passive person, are murdered because of Victor's monster and the revenge it wreaks on the world for being hated and rejected. A more Romantic version of a woman's death is Caroline's perishing merely from scarlet fever. Romantic elements also include the idealized De Lacey family who live in noble poverty in the woods. Gothic elements include their terror and violent reaction at the appearance of the monster.
In both Gothic and Romantic literature, a lone individual often emerges as central, but in Gothic, this character, such as Roderick Usher in Poe's Gothic short story "The Fall of the House of Usher," is apt to be suffering and unstable/evil, whereas in Romantic literature, the lone individual is likely to be flawed, but suffering and overall good.
Setting is important in Frankenstein, from woodland cottages to the icy arctic to lonely mountaintops.
Isolated settings are features shared by both Romantic and Gothic literature. In Gothic literature, for example, the isolated setting of the house of Usher is an important feature in "The Fall of the House of Usher," and Emily suffers terrors as she is taken to the remote castle of Udolpho by her evil uncle Montoni in Ann Radcliffe's Gothic novel The Mysteries of Udolpho.
Settings, especially those that show the power of nature and the sublime, are also important in Romantic literature. The sublime is that mixture of awe and terror that nature can inspire, the kind of feeling that arises when one, for instance, stands on an mountaintop and takes in the grandeur of the scene.
Setting in Gothic literature, however, tend to be remote and frightening, filled with the dark, gloomy, and foreboding, while Romantic settings, though they can sometimes be gloomy, are less about raising terror than about evoking melancholy or sadness. Romantic settings can also contain unabashed descriptions of the beauty of nature. For example, when Emily escapes the terrifying castle of Udolpho with its mysterious picture veiled by a black cloth, she arrives at a Romantic cottage where grapes grow outside her window. Wordsworth describes with sheer joy the beauty of daffodils dancing in the wind in his poem "I Wandered Lonely as A Cloud"
This is a big question, but in summary, both Gothic and Romantic literature share the themes of death and suffering and are prone to show women suffering and dying. In Gothic, the death and suffering are more likely to be due to murder and extraordinary circumstances, while in Romantic literature, death and suffering are more likely due to disease or more natural circumstance, such as getting lost on a dark night. In both genres, the lone individual tends to be a central character—though in Gothic, that figure is more likely evil or unstable, whereas in Romantic literature, he is most often a suffering but noble genius. In both genres, setting is of great importance, but the setting of Gothic literature is more likely to be terrifying, while the setting of Romantic literature is more likely to be melancholy or solacing.