Using Trypsin actually cleaves proteins that attach a cell to its substratum, while EDTA chelates the Ca and Mg ions that these cell attachment proteins need for maintaining the proper structural conformation required to do their function. Thus EDTA is a less damaging treatment compared to trypsin treatment. In experiments where immediate reattachment of the cells is required EDTA is preferred, while if you use trypsin, you must allow some time for the cell to make the cell adhesion molecules, transport them to the cell surface to replace the ones cleaved by trypsin. So trypsin treatment can be used for experiments that do not require quick reattachment of cells to the substrate. On the other hand Trypsin digest makes it easier to physically get the cells off compared to EDTA.
Using Ca/Mg free PBS and EDTA (to also remove Ca and Mg) is a cheap and easy way to detach your attached cells. Using trypsin will further expedite the process. I have used both before and they work well.
I have had long experience with both of them and I have obtained very good results with both ways, though those cells strongly attached to the plates were easily removed with trypsin.
EDTA easily chelate with Calcium and Magnesium ions and precipitate; under neutral pH these chelated molecules remains soluble which can be easily removed along with the solution hence PBS+EDTA is been used; Calcium and Magnesium molecules plays essential role in cell cell adherence and decrease the surface area for trypsin action ; Ionic gradient Ca+ Mg+ free buffers allows those calcium molecules to mix with the solution and enable more room for trypsin activity.
Using Trypsin actually cleaves proteins that attach a cell to its substratum, while EDTA chelates the Ca and Mg ions that these cell attachment proteins need for maintaining the proper structural conformation required to do their function. Thus EDTA is a less damaging treatment compared to trypsin treatment. In experiments where immediate reattachment of the cells is required EDTA is preferred, while if you use trypsin, you must allow some time for the cell to make the cell adhesion molecules, transport them to the cell surface to replace the ones cleaved by trypsin. So trypsin treatment can be used for experiments that do not require quick reattachment of cells to the substrate. On the other hand Trypsin digest makes it easier to physically get the cells off compared to EDTA.
I agree with all the answers. As trypsin cleaves protein, antigens on surface are also likely to be cleaved. So treating cells with trypsin will be an issue when you plan to analyse (immunostain) surface markers of the harvested cells. So care should be taken to minimise the digestion time. In those circumstances, I would use other agents which are less harsh and forgiving (EDTA, trypLE, accutase).
If you do not want to have an enzyme with animal origin, EDTA or trypLE would be a better choice.
Perhaps I could add, whatever the way used to detach cells,that it can be important to rapidly neutralize the agent as the cells have unsticked, and before to centrifugate them gently to remove trypsine or EDTA solution and obtain the pellet for further steps. In exemple dilute the suspension containing cells + enzyme or EDTA 1/2 fold in complete medium. I think that , for sensible cells (or first isolation from tissues for primary cultures), it's better. But only intuitive and by experience