Do you need to contain livestock or keep the neighbourhood yard apes out? 4X4 should be fine for a decorative fence.

Also consider wind and the ability of the fence to "vent" it.
A solid fence vs "alternating" construction.

Are you planning to buy 10' lengths and bury 4'? Not sure where you are in Canada but you'll want to be below the frost line so your whole fence doesn't heave after it's done. I guess I would use 4x4s.

Consider using 6x6 for corners and where any gates would attach. 4x4 works well for the other parts.

I presume that you have checked with the town/city/village that you live in, that six foot high fences are allowed under their fencing bylaw?????????

Lumber is sold by the board foot. A 4x4 is 16 sq. inches and a 6x6 is 36 sq. inches which is more than double the board footage and that means more than double the price per post.

Most fences of this height use 4x4's providing they allow a good deal of the wind to pass through them. If you are planning a solid fence, then the 6x6 would be a better choice. The other issue is the distance between posts. Putting the posts on six foot or five foot centers instead of eight foot centers, increases the strength of the fence when it comes to resisting wind.

The deeper you put the post, the more leverage it has over the area above grade. Another common error is to pour concrete around the post at grade level. All that does is make it easier for the frost to heave the post vertically out of the hole.

I would like to caution you about putting concrete around them. If you are planning to do so for strength be careful to not create a vase. Brick half in the bottom of the hole, tamp down with the post, adjust height with pea gravel if needed, back fill 1/4 with pea gravel for drainage, tamp, plumb, then a concrete collar, up to the freeze line, let set, then pea gravel. This will allow water to drain through, ice will crack the collar and water will rot the wood, if you make a vase.
If you just plan on putting the posts in the ground, get some pea gravel and river sand, mix 50/50 and use this to back fill, works great to sturdy the posts up.

I always leave them a little high to the level line and then cut to height if need be, easier than setting them to a line.

That was much more specific and good advice castoff and door.