You can use a t-test to assess if there are differences in the means. The different sample sizes don't cause a problem for the t-test, and don't require the results to be interpreted with any extra care. Ultimately, you can even compare a single observation to an infinite population with a known distribution and mean and SD; for example someone with an IQ of 130 is smarter than 97.7% of people. One thing to note though, is that for a given $N$ (i.e., total sample size), power is maximized if the group $n$'s are equal; with highly unequal group sizes, you don't get as much additional resolution with each additional observation.
To clarify my point about power, here is a very simple simulation written for R:
set.seed(9) # this makes the simulation exactly reproducible
power5050 = vector(length=10000) # these will store the p-values from each
power7525 = vector(length=10000) # simulated test to keep track of how many
power9010 = vector(length=10000) # are 'significant'
for(i in 1:10000){ # I run the following procedure 10k times
n1a = rnorm(50, mean=0, sd=1) # I'm drawing 2 samples of size 50 from 2 normal
n2a = rnorm(50, mean=.5, sd=1) # distributions w/ dif means, but equal SDs
n1b = rnorm(75, mean=0, sd=1) # this version has group sizes of 75 & 25
n2b = rnorm(25, mean=.5, sd=1)
n1c = rnorm(90, mean=0, sd=1) # this one has 90 & 10
n2c = rnorm(10, mean=.5, sd=1)
power5050[i] = t.test(n1a, n2a, var.equal=T)$p.value # here t-tests are run &
power7525[i] = t.test(n1b, n2b, var.equal=T)$p.value # the p-values are stored
power9010[i] = t.test(n1c, n2c, var.equal=T)$p.value # for each version
}
mean(power5050<.05) # this code counts how many of the p-values for
[1] 0.7019 # each of the versions are less than .05 &
mean(power7525<.05) # divides the number by 10k to compute the %
[1] 0.5648 # of times the results were 'significant'. That
mean(power9010<.05) # gives an estimate of the power
[1] 0.3261
Notice that in all cases $N=100$, but that in the first case $n_1=50$ & $n_2=50$, in the second case $n_1=75$ & $n_2=25$, and in the last case $n_1=90$ and $n_2=10$. Note further that the standardized mean difference / data generating process was the same in all cases. However, whereas the test was 'significant' 70% of the time for the 50-50 sample, power was 56% with 75-25 and only 33% when the group sizes were 90-10.
I think of this by analogy. If you want to know the area of a rectangle, and the perimeter is fixed, then the area will be maximized if the length and width are equal (i.e., if the rectangle is a square). On the other hand, as the length and width diverge (as the rectangle becomes elongated), the area shrinks.
