In this case it is better or from my sense I always make it by adding an inline style in the table and I think their no need to create any other style for it in CSS.
<table class="firsttable" style="text-align:left"> This is the firstable that must be left align
And the second table may be another inline style of text-align:center
<table class="firsttable" style="text-align:center"> And this is the second table that must be center align
It is the best approach. But you can also can create some different id here or
.firsttable:nth-child(1) { text-align:left; }
.firsttable:nth-child(2) { text-align:center; }
Problem in this is if you use it then if another table appear in this web page area than it will arise a problem. So it is better to use inline style in this case.