This question only applies in certain situations depending largely on the type and size or layout of your shower enclosure or space.
There are benefits and disadvantages to either layout depending on the circumstances so you should judge each by its merits depending on the situation that you are looking to use them.
A wet room is becoming more popular and its main advantages are that you don't need to step up onto a tray and that you can pretty much do whatever you want in the space that you have with regain to having an enclosure, shower screen or just an open room.
Without a shower tray you will need to water proof your room and work out how to deal with drainage.
Some people use large tiles or if you are on a ground floor which is solid this might be OK but will be harder to install drainage options.
The shower tray is the normal option as you but a shower enclosure and tray to match.
Now with much better stone shower trays on the market, you can get both high stone trays and low stone trays.
The low variety is better to look at but you will need to run the waste below floorboards whereas the high trays you have the option to run the waste under the tray and out of the side into a wall.
There are not many occasions where you will seriously have to choose between tray or wet room but you will now have a better understanding of the differences and when and where each option should be used.
Search online for huge ranges of shower trays or shower enclosures that can be used directly on the floor without the need for a tray.