I have used both softwares, and everyone who has used Photoshop first wouldn't recommend you to use Paint Shop Pro.
Paint Shop Pro is good, but Photoshop is even better in every aspect. If you are in the webdesign business, you will be asked to use Photoshop and no other software.

It's true. I can't see any job offer for webdesigners that doesn't require experiance in Photoshop. I wonder when will this change? Will it ever change?

Maybe not in this short term. However, I can't say that it will remain the same as more softwares will be develop in the future.

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Paint shops pro also have some cool features. But most of the designers use Photoshop because in Photoshop all the tools are very handy and there are lots of plugin’s available and it’s very easy to use. I suggest you should stick to Photoshop.