"Greek love" influences aesthetics or the means of expression, not the nature of Roman male-male erotics as such.
Both women and young men were considered normal objects of desire, but outside marriage a man was supposed to act on his desires only with slaves, prostitutes (who were often slaves), and the infames.
Gender did not determine whether a sexual partner was acceptable, as long as a man's enjoyment did not encroach on another man's integrity.
During the Republic and early Principate, little is recorded of sexual relations among women, but better and more varied evidence, though scattered, exists for the later Imperial period.
During the Republic, a Roman citizen's political liberty (libertas) was defined in part by the right to preserve his body from physical compulsion, including both corporal punishment and sexual abuse.
Although Roman men in general seem to have preferred youths between the ages of 12 and 20 as sexual partners, freeborn male minors were strictly off limits, and professional prostitutes and entertainers might be considerably older.
Same-sex relations among women are less documented.
The primary dichotomy of ancient Roman sexuality was active/dominant/masculine and passive/submissive/"feminised".
Roman society was patriarchal, and the freeborn male citizen possessed political liberty (libertas) and the right to rule both himself and his household (familia).
In the Imperial era, anxieties about the loss of political liberty and the subordination of the citizen to the emperor were expressed by a perceived increase in voluntary passive homosexual behavior among free males, accompanied by a documentable increase in the execution and corporal punishment of citizens.