Here is the solution based on the base package:
z <- lapply(intersect(df1$ID,df2$ID),function(id) {
d1 <- subset(df1,ID==id)
d2 <- subset(df2,ID==id)
d1$indices <- sapply(d1$dateTarget,function(d) which.min(abs(d2$dateTarget - d)))
d2$indices <- 1:nrow(d2)
merge(d1,d2,by=c('ID','indices'))
})
z2 <- do.call(rbind,z)
z2$indices <- NULL
print(z2)
# ID dateTarget.x Value dateTarget.y ValueMatch
# 1 3 2015-11-14 47 2015-07-06 48
# 2 3 2015-12-08 98 2015-07-06 48
# 3 3 2015-02-22 52 2015-03-09 94
# 4 3 2014-11-17 68 2014-12-15 95
# 5 3 2013-05-30 91 2013-04-01 85
# 6 1 2013-11-04 70 2014-02-21 35
# 7 1 2014-12-29 18 2014-12-06 88
# 8 2 2013-01-14 52 2013-04-08 77
# 9 2 2015-07-29 97 2015-08-01 68
# 10 2 2015-06-15 98 2015-08-01 68