Probably not much; he'd likely be only a figure head with less power than the British monarchy. I suppose though he would be viewed as another Franz Josef. Nit pick, he wouldn't be in the 88th year of his reign, as Franz Ferdinand would be in power for several years, then his father, who ITTL would have had the stress of being deposed from power inducing his heart attack. Maybe 40-50 years of reign though.
Less power than the British monarchy? Hardly imaginable. You cannot have a negative amount of power.
On the contrary, I believe that Otto would be among the more influential (rather than powerful) remaining European monarchs simply due to the high probability that His Majesty would still be needed in a multiethnic, yet democratic United Danubian Monarchy to mediate and to do a little bit more than to represent in order to keep things in order.
When compared to Spain, Sweden or the Netherlands, even to the UK, even an Austria-Hungary which is alive and well in 2010 needs the monarch as an integrating force and is less imaginable as a republic than the other examples.
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If allowed to die in bed, Franz Ferdinand might well live into the 1930s or even 40s. With good health, Karl I would reign until at least 1970 (taking the old age of his son and of Franz Josef into account, I suppose that Habsburg guys have a good chance to live quite long unless executed, shot, stabbed etc.). So Otto's reign would be long (as usual in Austria-Hungary), but not to an extreme.
By now, there is a high probability that, like in his OTL ruling of the "family", he would have stepped down in favour of his son.
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My thoughts on the odds of a survival:
- WW1, if happening, must not last into 1918; a CP victory might lead to overextension and is probably not the best of possible worlds; an early defeat which leads to a mini-monarchy consisting of e.g. OTL Austrian republic, OTL's 1942-Hungary, Croatia, Slovenia, German-speaking South Tyrol and Czechoslovakia might be just the optimal trimming and be a blessing in disguise.
- if an analogue to WW2 occurs, neutrality would be perfect. Austria-Hungary must NOT be in a defeated axis, and a being part of a winning Axis would not be helpful either IMHO.
- in any case, there must be no Sovjet dominance over Eastern Europe
- We do not need to discuss the need for gradual internal reform. By the way, I do not deem a putschlike reformation of Transleithania (i.e. the ruling political clique in Budapest) as a military matter which should make a German intervention even remotely necessary.