Take the implementation of as an example:

Approach I:

s=tf('s');
g1 = (s+1)/(s^2+s+1);
g2 = exp(-s);
g = g1*g2

Approach II:

g=tf([1 1],[1 1 1],'ioDelay',1);

Both the above two approaches give the following result:

Transfer function:
               s + 1
exp(-1*s) * -----------
            s^2 + s + 1