Yes, we are in basic agreement on both points.I don't think we actually disagree on either of these points. Many of Bismarck's successes were questionably attributable to his own actions (I'm thinking the role of the Mainz threat and the timing of Austria's defeat in Prussia's success in getting the South German states on its side). But Bismarck did have basic competence, which puts him about two-thousand miles ahead of Napoleon III.
As for the chassepot, I'm not saying that it was a gigantic advantage or that it could have let the French win the Franco-Prussian War, merely that its existence made the French army significantly stronger in 1870 than in 1866, though it's also fair to say that the French army vastly overestimated how important it would be. The point is that the 1870 French army was utterly outmatched by the Prussian army and that, consequently, the 1866 French army would be even more so.
Bismarck's gift was the capacity of making use of every possible advantage and integrate them into his main plan. It would be disingenuous to believe that he had based his strategy on Napoleon's making a ludicrous request or the Austrian being shattered so completely at Koniggratz: when these opportunities eventuated he made the best use of them. At the same time the generous terms offered to both the Southern German states and Austria in a moment when the Prussian armies were triumphant are "his" good choices (and even looking from the vantage point of 150 years in the future it would be very difficult if not impossible to make a better one.
I believe that Bismarck's record in the 1860s was impeccable; the 1870s were not too bad but not as good; the first Dreikaiserbund does smell of internal politics rather than showing a sweeping and long term international strategy;
the 1880s were a bit of a disappointment (but I admit that the feeling has something to do with what happened after that in Europe and Bismarck was getting a bit long in the tooth).
A war with the French army of 1866 would have resulted in a clear "no contest". Not only the French army would be without the chassepots, but also the lessons of 1866 would not have been digested yet.
King Wilhelm I of Prussia would have agreed with you; he wanted to march on to Vienna and only relented when Bismarck, whose use to Wilhelm lay in keeping the Landtag off the executive's back, threatened to resign. So all that you need for Prussia to attempt to make this happen is for Wilhelm I's erratic bursts of stubbornness and impetuosity to happen slightly differently at that one particular time. But as LordKalvan points out, other countries wouldn't be pleased by this development. If Prussia appears too dangerously powerful and expansionistic (and the annexation of Austria would mean actually wiping a great power from the face of the earth—it took the First World War and its millions upon millions of deaths to make that sort of thinking vaguely acceptable IOTL), the rest of Europe will start getting very afraid very quickly.
Some times history repeats itself. In 1859 after the unilateral armistice of Villafranca between France and Austria, Victor Emmanuel was almost ready to be bullied by Napoleon and to accept all the provisions of the peace treaty being discussed (which included a restoration of the dukes of Parma, Modena and Tuscany who had been ejected by popular insurrections). Cavour resigned and the king rushed to recall him back: even if Venetia could not be taken, Cavour managed the annexations of the former duchies and most of the Papal States. Not so different from the threatened resignation by Bismarck in 1866.
In 1866 Bismarck was the luck of Prussia, and the early death of Cavour proved to be the misfortune of Italy. If Cavour had lived another few years, the French meddling in 1866 would not have had the impact of OTL and the backseat driving of Victor Emmanuel would have been kept under control. The war on the Italian front would have been quite different.