The short answer is: Yes, if you are eligible. The Arexvy and Abrysvo vaccines are indicated for adults age 60 or older. Abrysvo is also indicated for women who are 32-36 weeks pregnant in order to protect the baby.
Respiratory Syncytial Virus (RSV) has been around a long time and can cause severe disease in those with compromised immune systems, particularly children and the elderly. However, unlike influenza, RSV is much more likely to cause long-lasting symptoms - respiratory physicians see every week children with permanent lung damage and asthma resulting from RSV infection they contracted in the first year of life. But although RSV does not cause long-lasting symptoms in adults as often as COVID, which causes symptoms lasting months to years in up to 25% of adults, older individuals infected with RSV can sometimes suffer long-lasting recurrent wheezing or asthma as well.
RSV is tricky to prevent - initial efforts at producing a vaccine in the 1960s actually did more harm than good. Some of those obstacles have been overcome, and although we still do not have an RSV vaccine for young children, Arexvy is the first RSV vaccine available to adults aged 60 or older. This population was targeted because of the severity of disease - nearly 180,000 people over age 60 have been hospitalized per year with RSV in recent years, and about 14,000 of them succumb to the disease. These aren't impressively high numbers among a nation of 330 million, so part of the question of whether to get vaccinated boils down to what one thinks about whether to take a chance on getting severe illness due to a disease for which we have a vaccine that does a good job at preventing severe illness. That also relates to exposure and the likelihood of getting infected. People who live alone and keep to themselves are much less likely to get infected than those who are frequently exposed to their young grandchildren.
For preventing severe disease, the vaccine does well. Vaccine effectiveness in the first year after vaccination was about 82%, which means that people who contracted RSV were about 5 times more likely to be hospitalized if they hadn't been vaccinated. Curiously, vaccine effectiveness dropped to about 65% in the second year after vaccination, whether a second dose of the vaccine was received or not. Ongoing studies will continue to examine this in order to determine a long-term vaccination strategy, but for now, it doesn't look like an annual revaccination will be beneficial, like it is for influenza and COVID. More information is required before making a decision in this regard. Abrysvo was similarly effective in the first year, but data on the protection in the second year is not yet available at the time of this writing.
For preventing RSV infection in infants during the first six months of life, vaccination with Abrysvo during weeks 32-36 of pregnancy was about 50% effective at preventing RSV infection in the first place, and about 80% effective at preventing severe disease.
In terms of side effects, they are the same as for most vaccines - the typical symptoms expected with strong immune system activation/mobilization, including fever, chills, and muscle aches. Arexvy contains an adjuvant, which is a substance known to help produce a strong, effective immune response (a "booster", if you will, although immunologists don't like that term because it means so many different things to different people). The adjuvant in Arexvy is the same as that used in the Shingrix vaccine, so if you have received the Shringrix vaccine, it is reasonable to consider that you'll have similar side effects with Arexvy, and likely not anything worse. Abrysvo does not have an adjuvant, and these symptoms of immune activation in the clinical trials were milder with Abrysvo than Arexy. But as with all vaccines that achieved approval for use, the risks associated with receiving the vaccine are far overshadowed by the benefits of reducing the risk of getting severe disease.