From someone who lived through it, there were a lot of nerves going into both the Islanders and Capitals series.
Islanders-Rangers hadn't played well in the Coliseum for a few years, Islanders always play the Rangers tough, and a lot of that Islanders team from 1993 that made the Cinderella run to the ECF was still there. The veterans the Rangers picked up at the deadline like MacT, Noonan, Matteau all had big series. The Rangers literally beat the crap out of them. Hit anything and everything. Hustled. The series would have probably been similar but if Healy was still the goaltender for the Islanders, it may have gone five or even six.
Capitals-One of the Rangers biggest rivals from 1986 to that point. In 86 the Capitals were a high powered offense missing Bengt Gustaffson who was pretty much the 80s version of Jiri Lethonnen (and hopefully Lias Anderson is the 2020s version of both

) Rangers upset them. 1990 with the Rangers missing Leetch, Capitals upset them. 1991 the Capitals upset them that led Smith to dismantle/alter his first core and bring in Messier/Graves/Beuk and the second wave of talented young guys. Pivonka. Johansen. Langway and his stupid 70s fro. Cicarelli. Liut. Names I hated as a kid. Capitals goal siren was one of the most annoying things to ever hear. This was the biggest pain in the you know what team. A few years earlier they played a game around Christmas 1991 when the Rangers were down 5-0 in the first, Richter was pulled, and they came back and won 6-5 thanks to Messier and Kris King. Rangers dominated the first three games but by game four the series the momentum shifted. Game 5 was not easy in any way, shape, or form. Richter gave up a bad goal. Leetch scored the clincher if I remember correctly on an outlet pass from Zubov.