Features of a non-periodic signal for comparison
It is just an idea but how about a mean of the terms in a sliding window. 

x = zeros(1,250);
c = randi(50,1,15);
x(c) = randi(500,1,15);
y = x;
d = randi(15,1,3);
y(c(d)) = 0;

figure;
stem(x,'LineWidth',1); hold on; stem(y,'LineWidth',1);
legend('Original Signal','Signal with Missing Samples');




N = 5;
L = numel(x)/N;
[m, m1] = deal(zeros(1,L));

for i = 1:L
    mx(1,i) = mean(x((i-1)*N+1:i*N));
    my(1,i) = mean(y((i-1)*N+1:i*N));
end

figure;
stem(mx,'LineWidth',1); hold on; stem(my,'LineWidth',1);
legend('Mean of x', 'Mean of y');




As you can see the plots are very similar now. You can also check their cross-correlation:

figure;
stem(xcorr(mx,my),'LineWidth',2);




These are of course just ideas to get you started. Now you can play with the window size and instead of doing $1:N$, $N+1:2N$ you can try $1:N$, $2:N+1$ , etc. and replace mean with other statistical parameters to see which one works the best for you.

Hope it helps!