How to make something like this?

How to make something like this? is it option in illustrator or photoshop?

Illustrator is the way to go - as it will be in Vector format - which means it can be scaled to any size without losing quality.
Creating in Photoshop usually means it will be Raster format - and the quality can degrade the larger the size it's increased to, depending on initial creation size etc.

Vector is the way to go.

It's very simple to redraw the emblem
The grunge effects might take a bit of time - and not suitable for all types of use, like embroidery

A coat of arms can be done in a number of ways, and can be digital or hand-drawn. Illustrator would be ideal although the lettering maybe be hand-drawn in that example.

That's a particularly grungy one and looks like it might have been badly Live-Traced to get that result, so may be difficult to recreate
unless you find the illustrator who did it of course.

But. How can i make countours like this?

I'd just draw them as they are.

I wouldn't think they are great design wise - this is where I'd have a fully clean one without those edges or grungy details.
Then had a grunge effects afterwards as another 'version' of the logo.

I can't imagine the grunge version being easy to embroider, but times have moved on since I was last doing it - I'm and old hat in the trade not in the trade much these days so my ideas may be outdated.

To me those look like the 'happy accidents' you get when you Live Trace a low res or hand-drawn image to vectorise it.
Or a filter has been used along the line, there are various ways it can be done.

It depends what you want to use it for, but I personally think grunge looks better in Photoshop and maybe with hand-drawn images.