handheld vs console?

Handhelds generally have more limitations because of their size, but some of the games can be incredibly fun and handhelds can be played just about anywhere because of their portability. Consoles usually have much better graphics and tend to host more complicated games, but they're not really portable and can cost a lot more than a handheld. If you like one, you'd probably like the other as well.

Best for what? They're different devices for different uses.

If you want portability and maybe the ability to play solely on battery power then use a handheld console. If you want the latest and most feature-rich games then no portable device is suitable and so you need to use the power of a console. Or even the thing you didn't want mentioned...

Your choice.

Console games are really fun and you can play the games on bigger screen tv

Why would you put this in the PC section if you don't want PC to be the answer?

Anyways a modern console is far more powerful than a modern handheld so the console is better at gaming. You also have controller options and a much larger screen.

I think PSP is the most powerful handheld device it will help you to play anywhere but it little bit less in terms of graphic quality. In console I think XBOX ONE is the best

Console gaming will you give you a more powerful gaming experience and flexibility of game types and quality, however handhelds will be capable of gaming anywhere with slightly decreased quality in game, however if your into controllers and such there are types of controllers which you connect to your handhelds. Hope this helps.