I recently put up a table of "flight" competition (distance shooting) from a few years ago involving various kinds of bows...
Not representative since these are modern bows and other equipment and specially-designed arrows... Ranges are pretty impressive.

I seem to recall from books like The Gray Goose Wing that typical self "warbows" like the Engiish longbow were capable of ranges further than that.. Somewhere around 300 yards.  That's ultimate range, however, and not effective range which is what I believe your figures would be close to.

The Asian composite/recurve bows were typically capable of much longer ranges; but they also used much lighter and more aerodynamic arrows.  600 yards +, as I recall.   Turks held all flight records for many years in the past.

A lot of your ranges will be dependant on what type of self bow and what type of composit bow, they vary widely.  An English longbow shooting one of the super heavy war arrows would be lucky to go 200 meters, the same bow with a distance arrow would add about 100 meters more.  The NA plains bow which was designed to shot from horseback is very short with a very short draw length, from my limited experiance, I would agree with De. Pope.  An Eastern Woodland bow from the same time frame, which was longer and used a longer draw, will shoot an arrow 50 to 100 meters further. 

And some of those bows that Dr Pope tested were composite, he didn't include those in his summary because they all broke when he attempted to string them.  The glue had gotten brittle over the years they had been sitting in the museums and they all delaminated.

Basically, an arrow starts to slow down as soon as it leaves the string, so a bow with a longer draw such as the Asiatic composites with their very long draws will outperform a shorter drawing bow.  The only selfbow that I am aware of with a comparable draw length is the English longbow.

Here some ranges
http://www.bogensport-rheinland.de/html/2_6__rekorde.html#Landesrekorde

Michel

Thearos wrote on Mar 28^th, 2013 at 4:29pm:

Well... Look up the flight contest between an african man using his standard hunting gear and saxton Pope with his finest yew longbow and flight arrows. The first shots of the African went further than Pope's flight arrows. Then Pope used his heaviest yew longbow and was only able to beat him by a few yards.
I think a 125 pound English warbow can chuck an arrow pretty dang far, Thearos. Keep in mind TBB- an arrow shot from a 70 pound bow 75 yards away arrives as fast as an arrow shot from a 50 pounder at 25 yards.
at around 125 yards a warbow would be equally tamed"
That is not an exact quote, but i think the distances are correct...
http://www.archery.org/content.asp?id=892&me_id=753&cnt_id=895
Here are some cold, hard facts.
-Squirrel

If Cretan archers were using short, thick flatbows, around 5 feet (1.3m) or so, and very heavy arrows, then their arrows would probably not go much past 125m or so.  Especially if they were pinch drawing to under the chin.  Are there any drawings or paintins of a Cretan archer?  Especially of ones shooting?

Lots of old info on distance shooting here: http://www.archerylibrary.com/books/badminton/docs/chapter24/chapter24_1.html

I recall, but haven't yet fount the reference for, one of the English kings decreeing that the shortest distance a man should practice at is 220 yards.

There are plenty of 300+ yard shots here with flight arrows, but more significant is 240 yards with a Mary Rose bow and a quarter pound arrow: http://www.theenglishwarbowsociety.com/records2012_EN.html

Ottoman flight shooting is still top,as far as i know.
Many 800+m shots the best being somewhere 840-850m They used bows 130-150# with ~15g arrows around 60cm long and siper-overdraw technique.