First of all, the charges will vary bank to bank so there is no exact amount that can be given to your question.
However, depending on your choice of banks at either end, the following charges can apply:
1) Money transfer charges - from your bank
2) Correspondent (middle) bank charges - Your domestic bank may not have a direct relationship with the receiving bank which is usually the case involving FX transfers. This is why a correspondent bank is used i.e. the domestic bank has an account with a correspondent bank dealing in the end deposit currency (based in the receiving country or offshore) to which the money is sent and then the correspondent bank relays it onward into the destination bank account. They charge a fee for this
3) FX movements and the bank commission for purchasing / selling FX on your behalf. Both AED and SAR may be pegged to the USD but the rate between these currencies itself varies. Not a lot but it varies and in addition, the conversion of your domestic currency to the FX attracts a commission from the bank when it buys or sells forex. To give an example, on the street in Bahrain, 1 Bahraini Dinar is exchanged for 10 SAR. What I mean is that in Bahrain, Saudi currency is accepted for everything since a lot of them come over the causeway (and you get change back too in SAR ). However, when you transfer through banking channels, you can get rates anywhere from 9.6 to 9.9 (never the full 10) depending on how the inter-currency rates are moving. For most of 2018, I was getting hit on transfer from Saudi to Bahrain as I was getting a rate between 9.7 and 9.8. Since early 2019, I am getting 9.9
4) Receiving charges by the bank where the money is going to be deposited
And the 155 AED that you are referring to; it is most probably correspondent bank charges as well as the loss in FX (AED is stronger than SAR i.e. it is not a 1:1 relationship. Today 960 SAR will get you 940 AED on the open market without commission) plus FX commission from the bank.
Globally, correspondent bank charges range between 25 to 75 USD per transfer. There are no charges from the UAE Government. SABB is probably using HSBC Middle East as their correspondent bank which charged you this money to send the funds onward to ADCB as SABB probably doesn't have a direct relationship with ADCB (To keep it simple, when you send money to ADCB, it is first sent by SABB to HSBC where it is deposited in the bank account of SABB with HSBC. Then, another transfer is done by HSBC to ADCB). If you had the account in HSBC Middle East itself, you wouldn't have been hit by these charges as detailed in point 2 above.
On a transfer of 150K SAR, I would assume:
Sending charges 40 SAR
FX loss in conversion to AED close to 3,000 SAR (as per today's open market rates. Could be more on inter-bank rates combined with commissions)
Correspondent bank charges from 100-200 AED
So to make sure you get 150K AED in your account after covering charges, send something like 154K SAR.