How Do You Make a Comparative Stem and Leaf Plot in R?

Have a look at stem.leaf.backback of the aplpack package. It sounds like that may be what you are looking for.

> a <- c(5.9, 7.2, 7.3, 6.3, 8.1, 6.8, 7.0, 7.6, 6.8, 6.5, 7.0, 6.4, 7.9, 9.0, 8.2, 8.7, 7.8, 9.7, 7.4, 7.7, 9.7, 7.8, 7.7, 11.6, 11.3, 11.8, 10.7)
> b <-c(6.1, 5.8, 7.8, 7.1, 7.2, 9.2, 6.6, 8.3, 7.0, 8.3, 7.8, 8.1, 7.4, 8.5, 8.9, 9.8, 9.7,14.1, 12.6, 11.2)
> stem.leaf.backback(a,b)
_________________________________
  1 | 2: represents 1.2, leaf unit: 0.1 
            a       b        
_________________________________
             |  5* |             
   1        9|  5. |8        1   
   3       43|  6* |1        2   
   6      885|  6. |6        3   
  11    43200|  7* |0124     7   
  (6)  988776|  7. |88       9   
  10       21|  8* |133     (3)  
   8        7|  8. |59       8   
   7        0|  9* |2        6   
   6       77|  9. |78       5   
             | 10* |             
   4        7| 10. |             
   3        3| 11* |2        3   
   2       86| 11. |             
             | 12* |             
_________________________________
                    HI: 12.6     
                    14.1         
n:         27       20       
_________________________________

Setting the m parameter to 1 gives:

> stem.leaf.backback(a,b,m=1)
___________________________________________
  1 | 2: represents 1.2, leaf unit: 0.1 
                  a      b              
___________________________________________
    1             9|  5 |8             1   
    6         88543|  6 |16            3   
  (11)  98877643200|  7 |012488        9   
   10           721|  8 |13359        (5)  
    7           770|  9 |278           6   
    4             7| 10 |                  
    3           863| 11 |2             3   
                   | 12 |6             2   
___________________________________________
                         HI: 14.1           
n:               27      20             
___________________________________________

The basic stem function has no support for this. It would be easier to do a histogram as @pbible pointed out (although, not much easier if you want them back to back). But you could do

#sample data
x<-list()
x[[1]]<-c(5.9, 7.2, 7.3, 6.3, 8.1, 6.8, 7.0, 7.6, 6.8, 
    6.5, 7.0, 6.4, 7.9, 9.0, 8.2, 8.7, 7.8, 9.7, 7.4, 7.7, 
    9.7, 7.8, 7.7, 11.6, 11.3, 11.8, 10.7)
x[[2]]<-c(6.1, 5.8, 7.8, 7.1, 7.2, 9.2, 6.6, 8.3, 7.0,
    8.3, 7.8, 8.1, 7.4, 8.5, 8.9, 9.8, 9.7, 14.1, 12.6, 11.2)

#specify common breaks
brx <- pretty(range(unlist(x)), 
    n = nclass.Sturges(unlist(x)),min.n = 1)

#calculate bins
h1 = hist(x[[1]], breaks=brx, plot=FALSE)
h2 = hist(x[[2]], breaks=brx, plot=FALSE)

#draw
plot(NA,NA,type="n", xlab="", ylab="",
    xlim=range(c(-h1$counts, h2$counts)),
    ylim=range(brx),
    xaxt="n"
)

rect(-h1$counts, brx[-1], 0,  brx[-length(brx)], col="blue")
rect(0, brx[-1], h2$counts,  brx[-length(brx)], col="red")

axis(1, at=axTicks(side=1), labels=abs(axTicks(side=1)))

which gives you

And if it really needs to be stem and leaf style, here's a fragile attempt

x<-list()
x[[1]]<-c(5.9, 7.2, 7.3, 6.3, 8.1, 6.8, 7.0, 7.6, 6.8, 6.5, 7.0, 6.4, 7.9, 9.0, 8.2, 8.7, 7.8, 9.7, 7.4, 7.7, 9.7, 7.8, 7.7, 11.6, 11.3, 11.8, 10.7)
x[[2]]<-c(6.1, 5.8, 7.8, 7.1, 7.2, 9.2, 6.6, 8.3, 7.0, 8.3, 7.8, 8.1, 7.4, 8.5, 8.9, 9.8, 9.7, 14.1, 12.6, 11.2)

X<-stack(setNames(x, c("a","b")))

brx <- pretty(range(X$values), 
    n = nclass.Sturges(X$values),min.n = 1)

X$stem <- factor(brx[cut(unlist(x), breaks=brx, include.lowest=T, labels=F)], levels=brx[-length(brx)])
X$leaf <- as.integer(X$values %% 1 *10)


max.leaf.width <- 2*with(aggregate(leaf~ind+stem, X, length), tapply(leaf, ind, max))

fmt<-paste0("%", max.leaf.width[1],"s | %2s | %-", max.leaf.width[2],"s")

va<-with(subset(X, ind=="a"), tapply(leaf, stem, function(x) paste(rev(sort(x)), collapse=" ")))
vb<-with(subset(X, ind=="b"), tapply(leaf, stem, function(x) paste(sort(x), collapse=" ")))

va[is.na(va)]<-""
vb[is.na(vb)]<-""

cat(paste(sprintf(fmt, va, levels(X$stem), vb), collapse="\n"), "\n")

Which produces

                 9 |  5 | 7         
     7 7 5 4 2 0 0 |  6 | 0 0 5     
 9 7 7 7 7 5 4 2 2 |  7 | 0 2 4 7 7 
           6 1 0 0 |  8 | 0 3 3 5 9 
               6 6 |  9 | 1 6 8     
                 6 | 10 |           
             8 5 3 | 11 | 1         
                   | 12 | 5         
                   | 13 |           
                   | 14 | 0