I know a couple guys that have one but never seen one used in the field. The 30-30, 308, 30-06 and a few 300 savages have the popularity around here.
Don't see why it wouldn't be a fine hunting round.
What is the popular bullet weight in the 303 brit?

Bullets are usually in the 180-190 gr range and the caliber is excellent under 250 yds. Most guns are army surplus so accuracy is sometimes an issue, more from the rifle then the caliber.

It sounds like it is very similar, in performance, to the 300 savage.

My uncle has old 303 brit that his father gave him. I have asked several times to let me have it but oh no. I shot it once and it was similiar, as in recoil to the .308. He has taken numerous deer that were feeding in his garden and he isnt much of deer hunter. The .303 I believe is in a class of its own. Just an old collector with good knock down power if kept in good range. ALthough its pretty hard to find .303 ammo at your local wal mart.

The 303 British is stil live and well in Canada and has quite a history with various makers. The Old Army 303 Lee Enfield had it's share of problems with the actions and a company in Long branch ,Ontario quickly fixed the problem and manufacuted what was known as "the long branch action" They had ten of thousands produced and suddenly WW 2 was over.
The Log Branch actions were then married to Shiling(spelling) barrels made in England and hehseforth the birth of the "modern 303 Brit."
These 303s were as dependable,accurate and reliable as anything else close to the calibre produced since. Quite amazing when you think of it.
That's only a little bit of 303 brit history that I'm aware of....

I think the British and Canadians used the Lee Enfield .303 in both world wars.
I'm sure millions were produced,I've seen them everywhere here in my life,as they were all sold off as surplus.I believe they were made from a Mark 1 to a Mark IV. A truly durable gun,but many I have seen were in sad shape..
The .303 is quite a capable cartridge,typically sold now loaded with 150 to 180 grain bullets,still available anywhere here. I think slightly less powerful than a .308 or 30.06...
Just a note of interest;
The infamous "Mad Trapper" Mike Oros (Finally killed about 1983) used this gun and calibre exclusively, to kill more than big game... Read the book "Decent into Madness"