It depends of the exercises. You can do a curl or lateral raises at maximum performances even if you are very tired. It's harder to do a Deadlift or a Power Clean & Push Press BUT you are right I changed my mind. When I did the PC & PP I used 80% of my 1RM and it was not enough... I was losing strength that's why I had the feeling my workouts were harder. Now I Deadlift everyday a 90% and I used to DL at 95% everyday without any problem, tired or not.
If I had to do a 1RM without sleeping enough for a few consecutive days maybe that I would be a little bit weaker or not... If you don't sleep at all or only a few hours for several days in a row you'll be MUCH weaker, no doubt about that but in "normal conditions" there are very little variations in strength.

Workout n°25

Deadlift : 152.5
Floor Press L/R : 41
Curl L/R : 25/24.5

Everything was easy. It's much more easier at 90% compared to 95% and normally the stimulation should be the same with less fatigue and thus no more fatigue accumulation, no more overtraining. IF it's not the case I'll have to decrease my frequency or take a week off here and there but I think it's not necessary if the load is optimum : MAX FORCE - MIN TIME/fatigue.