This topic has come up once or twice in the past, but a little review now and then never hurts. The instrument that you are referring to in light aircraft is a Turn & Bank Indicator or a Turn Coordinator. The purpose of either of these instruments is to show, both the rate of turn (When the aircraft or needle is on the index or mark, the rate of turn is equal to 3 degrees per second or "Standard Rate".) and the "quality" of the turn. (If the ball is centered the turn is coordinated, if it is not centered the aircraft is in either a slip or a skid.)
A little bit of background information...
The AIM states that a pilot will make all turns at:
1. 3 degrees per second, or
2. 30 degrees of bank angle, or
3. 25 degree bank provided a flight director system is used.
It goes on with the following note: Use which ever requires the least bank angle.
Like I mentioned, the turn rate for jets (assuming that they are equipped with a flight director) is based on a maximum bank angle of 25 degrees. On certain aircraft, this bank angle is further reduced at high altitudes. For example, many jet aircraft are programmed to use a maximum of 25 degree banks up through about FL300 where the bank angle is reduced to about 20 degrees. In practice, the actual bank angle achieved in a given turn is a function of the number of required degrees of turn. The ratio is normally about 1:1. For example, if you've got a 10 degree heading change you'll typically see a 10 degree bank. A 5 degree heading change would result in a 5 degree bank. A 35 degree heading change would result in the aircraft banking to its limit - 25 degrees down low and 20 degrees up high.
In turbojet aircraft there is really no such thing as a "standard rate" or 3 degree per second turn. As you noted, we don't even have Turn indicators or Turn Coordinators on the panel, just a couple of simple "bubble" slip/skid indicators under the EFIS displays and/or a couple of electronic slip/skid indicators built into the displays themselves.
Why? It's pretty simple really. As airspeed increases, it is necessary to use a greater angle of bank to maintain the same rate of turn. Without a turn coordinator installed in the cockpit we have absolutely no way of determining what our actual rate of turn is - without resorting to the use of a stop watch. Put another way, if you take two aircraft in a 20 degree bank, one flying at 350 KTAS and the other one flying at 130 KTAS - the faster aircraft will require 5.3 minutes to complete a 360 degree turn while the slower one will complete it in 2 minutes. The faster aircraft will also have a turn radius approximately 9 times that of the slower airplane. So you see how a standard rate turn would would pretty well for an airplane flying up to about 250 knots or so; but you can also see what would happen if he had to turn at 3 degrees per second at our normal cruise speed of 470+ knots.
There is a rule of thumb that will get you in the "ball park" when it comes to determining what angle of bank will be required to establish a 3 degree per second turn. You simply take 1/10 of your airspeed and add 5 degrees. Holding at 200 knots would require a bank angle of +/- 25 degrees. If you are able to hold at a slower speed, say 180 KIAS, the required bank angle would be slightly less (23 degrees), but again from the cockpit we really have no way of knowing what our actual rate of turn is - so we just go for the 25 degree bank angle that's programmed into the F/D. Could we take away the F/D and go with a 30 degree bank? Sure but most people try to limit bank angles for passenger comfort.
As a side note, The feds took all of this into account when they came up with the various holding speed limits. They are there to keep you from leaving protected airspace during the hold.