It usually depends on the controller of choice. Most controllers will only work with 1 type or another. Some will give you a choice.
10K type 2 and 3 are the most common but Honeywell uses 20K on some controllers. Alerton used to use 3K on the older stuff. Tridium I/O modules have profiles for 10K type-3 built in but tables can be entered to use a variety of types.
1K is uncommon as a thermistor (Negative Temperature Ceofficient). RTD type sensors are very common in the 1K range but can have different characteristics (Nickle Iron vs Platnium).
This is the problem that I currently having with one of the system. I had an old Carrier A/C unit and it was enabled (off/on) by a 20/20 system. 20/20 system was able to check return and supply air temp. I replaced the A/C unit and added new supply and return air thermistor to the new unit for the 20/20. I assumed that the thermistor were 10k and replaced with 10k as well. Now the reading is way off at the 20/20 system. These are the new temperatures reading. Supply air temp 19 F and Return air temp 16 F. I know for a fact that those are not the actual temp reading at the unit. I don't have access to the old system to check the old thermistor.
You need to figure out what sensors the 20/20 used or install a new controller. If you need information on sensors I buy them from BAPI (Building Automation Products Inc.). If you go to their website http://www.bapihvac.com/ and look on the bottom left there is a link for Sensor Specs that may be helpful once you get the info on the 20/20- is that a Carrier Product?
You can try using 5k Thermistor for carrier chiller unit. if not you have to measure the sensor resistance and download some of the temperature-resistance table and compare, roughly you will know which sensor type. From my opinion, for slow process control such as air conditioning use of thermistor is better than RTD, whereas for fast control process like steam control then RTD is more appropriate. Both thermistor and RTD have an accuracy range over the temperature, therefore depend on what application and check on the sensing temperature follow by select the correct temperature sensors.
The 20/20 system was our legacy product and only takes dry contacts or 4-20 ma. PM me and tell me what module it is 8/8, P10 etc... possible newer next gen z-line like Z540v that takes a thermistor 10k-2 but the software was Supervision then and Ill send you the spec sheet.