In term of price and time, SELEX on protein should be more advantageous, furthermore, although with counter selection you could select aptamers against many different proteins using cell-SELEX. However, as mentioned by Paromita you have to be sure that your protein as a good conformation. A good solution could be crossover SELEX mixing step of cellSELEX with step of selection on protein
At Base Pair Bio we perform custom aptamer discovery services. As stated previously, in our experience with protein SELEX, you run the risk of the protein not being in its native conformation or the epitope the aptamer binds to being hidden. The advantage is that protein SELEX is well-characterized. Meaning a lower price and reduced time.
A practical disadvantage of Cell SELEX lies in the ability of the researcher to properly express the protein, thereby increasing the turn around time. In comparison, recombinant proteins are simpler to obtain. Also, you run the risk of selecting aptamers against other things in the cell and not the target protein. The advantages of Cell SELEX being that the protein is in its native conformation and the aptamer is selected under native conditions, increasing the likelihood of finding an effective aptamer.
There are a couple ways to work around the disadvantages, such as doing a combination of both methods or employing liposome based methods (e.g., Integral Molecular's Lipoparticles), which are very expensive but potentially saves time.
It depends on your purpose. Suggest you to read some reviews on these topic and then you may know which one is more suitable for your real situation. For example, Prof. Tan's group is quite good at cell SELEX, for your information: