There was actually a thread not too long ago where we spent a long time talking about the differences in NDLs depending on the model/algorithm used. They can be substantial. This really goes to the fact that decompression is a mathematical model of an incompletely understood physiological process. Different assumptions are made in the construction of different models. Some look only at dissolved gas, some look at bubbles. Some mix the two.
The bottom line is that where you go into deco is imprecise.
What's important about your opening post is that, according to your dive information, you are a new diver. You really shouldn't be pushing your limits to put yourself into deco, whether real or a figment of your computer's imagination. Do you know how to calculate whether you have enough gas to be as deep as you were for as long as you were, and still DO your 8 minutes of deco? Do you have the buoyancy control to be able to do the deco? Do you know whether you should have done deep stops, or why one would do deep stops, or where you would do them?
There is a ton of stuff to know about diving with decompression obligations. Being caught between the necessity to decompress and an inadequate gas supply to do so is a recipe for an accident. The best way to avoid that is not to push your limits so hard, so early on. If your divemaster was working for a commercial operation, he should have stressed that you watch your computer and let him know when you were approaching your NDLs. If your divemaster is a friend, he should know better than to let you go into deco at your stage of the game.
Now, we could also get into dive planning, and whether you checked to see if the profile proposed for the second dive was going to fly from an NDL standpoint, but from experience, I know that planning multi-level dives is difficult because there aren't many tools with which to do it. If you use the tables, the first dive put you into deco and would make you stay out of the water altogether for the second one. I don't know what you would come up with if you used the PADI wheel, because I've never used it.
Anyway, I think there are some more important questions to be asked here than what the differences between the computer algorithms are.