Why do rich people prefer shares with dividend over bonds?

Generally, all securities on the market can be analyzed for their dividends vs growth potential, and this is called Value on the high-dividend end, and Growth on the low-to-no dividend end; of course this is a continuous scale.
Some investors prefer Growth investment, others prefer Value investments. It depends a lot on their personal situation, and their needs, for example the need (or not-need) to a constant income stream; and it also depends on their personal preferences and risk acceptance.

Overall,

• if you want a constant income stream (because you are living from it), Value investments have some advantage, and are often preferred.
• If you don't need the money for years, Growth investments are often preferred - they have wilder swings, but better overall return expectations.
• You can of course also split your investments in any way between the two, depending on your preference and needs.

The second dimension is Risk - all securites on the market can be classified by their risk. Typically, higher risk comes with higher expected gain (though not always).

The two dimensions are orthogonal, meaning independant of each other.

Bonds are a different risk class of investment than shares/fonds, and generally have a much lower risk - and equally lower income expectation.
A bond might give you 2% with high confidence, whereas shares with dividends might give you 6% with some risk (and Growth shares 9-10% with a lot of risk).

That should make it obvious why you wouldn't invest all in bonds if you're rich - you don't need all the money right away (if ever), and you get a lot more profit by investing in higher risk classes.

Simple.

Difference between shares and bonds:

• By owning bonds, you just hold some generic instrument that is supposed to yield a particular amount but you never know that in case of junk bonds. Quality bonds yield little, so the only way to make real money with bonds is by purchasing junk bonds (I won't recommend that, though)
• By owning shares, you own part of the company and its future income.

For example, if I think the clean energy sector is a very important sector due to climate change concerns, by buying clean energy bonds I'll most likely get its nominal yield. By owning clean energy shares, there's a potential for massive profit.

If I think climate change concerns benefit forest, by buying forestry company bonds I'll most likely get its nominal yield. By buying forest and forestry company shares, there's a potential for massive profit.

Add that difference to the historical observed result that stocks yield more than bonds, the choice should be clear.

Not-so-rich people may have a lot of government bonds or cash in their portfolios because relatively speaking the need for an emergency fund that should consist mostly of very liquid instruments is larger.

Actually, in the long run, risk with stocks may be smaller than with bonds. Stocks can drop 80% and are expected to yield 8%. Bonds can drop perhaps 10% and are expected to yield 4%. In 43 years, you are 99% certain to have a larger amount of money with stocks than with bonds. Oh, and currently bonds don't yield 4%, they yield about 0% (at least in Europe). Stocks don't yield 8%, they yield perhaps about 7%.

I don't think rich people will prefer shares(stocks) with dividend or even bonds. Because in both these cases they will need to pay taxes.

I think rich people will prefer non dividend paying , high growth stocks with high beta.

For middle class should look at asset allocation

The question seems to assume that bonds and stocks are nearly perfect substitutes for each other. They are not. They are exposed to different risks (market risk vs. interest rate risk, primarily) and have expected rates of return that correspond to the market's pricing of that risk.

There are gains from diversifying across stocks and bonds, so I would say that most rich people who are investing wisely are investing in both stocks and bonds. Saying they prefer one over the other is like saying they prefer Exxon over Microsoft. Some people might tilt their portfolio toward one or the other for whatever personal reason, but the smart thing to do is own both. That's the general principle.

Now, is there a reason why rich people right now might be tilting away from bond ownership? Yes, there might. Bonds at the moment are so highly priced that a shocking fraction of them (globally) have negative expected return. There are many investors (like pension funds) who are forced to continue to buy bonds and support these prices. It may be that high net worth individuals are shying away from bonds at the moment because of their high price, but this is not something you should expect to always be the case.

You may also have the impression that rich people buy stocks because certain rich people, like Buffet, buy controlling shares in a company and use their voting power try to change/improve the company. But this behavior is distinct from a standard, passive, investing strategy, like Bill Gates follows.