What is a difference between [gen] and [gen~]?

there's no increase in precision, and it's not really about being less CPU heavy(some standard Max objects might be more efficient than if you worked your own math in 'gen'... but maybe you meant less CPU heavy than 'gen~'..)
if i recall correctly, it was just a convenient addition: 'gen~' was the initial environ, offering sample-accurate operations, 'gen' took that same environ and offered those operations in the event realm(the only difference is 'gen~' is on the audio scheduler, while 'gen' is on the event scheduler)

Sorry, I am a bit confused by the answer. I completely understand the purpose of [gen~] but I still don't understand the purpose of [gen] (event realm).

I'll try to ask differently.

When should I use [gen] (event realm) instead of classic Max objects? What is the main advantage of [gen] (event realm) when it's running with the same precision as classic Max objects?

Thanks!

When should I use [gen] (event realm) instead of classic Max objects?

if you can do what you want with classic Max objects, then only use those, otherwise use [gen](event realm) all other times.

What is the main advantage...?

none. you can write math in a different way, more concisely, it can also attach to a clock differently, and allows for easier programming('easier' is just my opinion), but most things can be done without gen-event-realm anyways.

Ah, OK! So I guess main advantage of gen(event realm) is codebox, right?

EDIT: Advantage when compared to classic Max objects I mean.

ya, codebox makes things there more like a regular programming language. more concise. that's an advantage. if you needed a sine wave or a phasor or other signal-like operations, but translated to event-math, that's another advantage.
but you could still do these things with classic Max objects... gen-event-realm simply makes it easier to program because the math is expressed in a more logical way - codebox is also called 'genexpr', which is also like the classic Max object: 'expr'(see helpfile)... so you could also see an advantage that gen-event-realm is like a nicely extended version of the 'expr' object.

I see. Thanks a lot, Raja!

I've used gen for things that don't need to happen at audio rate.

For example, to initialize the content of a buffer~ that happens once (e.g. setting up an impulse response, filter coefficients, window function, etc.), rather than using a codebox in gen~ with some kind of once-only wrapper (like if(elapsed==0) {...}, which is my usual trick) or a wrapper that only happens very sporadically (again, rather than writing if(changed(someparam)) {...}). Another example where I used gen was my 'turn midi events into a byte buffer' patch, which again meant responding to sporadic events and writing into a buffer~.

One very specific advantage of the latter is that gen can trigger processing for more than one incoming message event per audio sample clock, whereas gen~ will only poll param values and will only process the algorithm once per sample clock.

Also, if you happen to have got more used to writing in gen~ than MSP, then gen can be a handy space to have to complement it :-)

The biggest advantage of using gen in the event domain is the use of mc.gen. For example, this could allow me to have 100 counters without having 100 counter objects.