I agree with 小玲 on "我看了两次了”seems that you are telling the truth simply.but “我看过了两次了”depends on different cases.you can change your tone to show you really like something or you're fed up with sth.

I think they are almost the same. If u really want to find the difference between them,I think that it is the tone. “我看过了两次了”seems a little impatient, but"我看了两次了”seems that you are telling the truth simply.

the difference acutually we do not exactlly feel for chinese people when we are speaking. if we have to find out the difference , i think it just like past tense & perfect tense 看过 just like "saw" 看is a verb / normally 过=ed ， for example 吃过， 想过， 看了 just like "have seen" you can also say 我看过了两次 that is pluperfect tense

there is no different between those two sentences

the same meaning